Applications Using Linear Models

Key Questions

• How do you create a linear model in a word problem?

  To find a linear function (model), we need two pieces of information:

  #{("Point: " (x_1,y_1)),("[Slope](http://socratic.org/algebra/graphs-of-linear-equations-and-functions/slope): " m):}#

  So, find them from the description of the problem, then use Point-Slope Form

  #y-y_1=m(x-x_1)#

  to come up with the equation.

  ---

  I hope that this was helpful.

  Wataru · 1 · Nov 7 2014
• What are some Applications Using Linear Models?

  The major practical application for linear models is to model linear trends and rates in the real world.

  For example, if you wanted to wanted to see how much money you were spending over time, you could find how much money you had spent at a given time for several points in time, and then make a model to see what rate you were spending at.

  Also, in cricket matches, they use linear models to model the run rate of a given team. They do this by taking the number of runs a team has scored in a certain number of overs, and divide the two to come up with a runs per over rate.

  However, keep in mind that these real-life linear models are usually always averages, or approximations . This is just due to life being so random, but we never actually stick to those rates we have. For example, if a cricket team's run rate was judged to be 10.23 runs per over, it doesn't mean that they scored exactly 10.23 runs every over, but rather that they scored that many on average.

  Hope that helped :)

  Darshan Senthil · 1 · Feb 17 2015
• How do you define your variables when given a word problem?

  Answer:

  A general approach is to let the variable be whatever the question asks you to find......

  Explanation:

  A general approach is to let the variable be whatever the question asks you to find......

  Find the number. Let the number be #x#

  How many toys does Pete have? Let the number of toys be #x#

  What is the price of the shirt? Let the price be #x#

  If you are asked to find two numbers,
  or the length and breadth of a rectangle
  or the ages of a mother and her son
  or the price of pears and peaches, then.....

  Let the variable be the smaller number and then write an expression for the other value.

  When each unknown has been defined with a variable, then write the equation.

  e.g. The sum of two numbers is 15:
  Let the smaller number be #x# and the larger be #15-x#

  The sum of three consecutive numbers is #57#
  Let the numbers be:#" "x," " x+1," " x+2#

  Sometimes you will not be given a specific relationship between the numbers. In this case use two variables.

  Let the numbers be #x and y#

  EZ as pi · 1 · Jul 19 2018

• What are some Applications Using Linear Models?
• How do you create a linear model in a word problem?
• How do you write an equation in slope-intercept form to show that Andrew puts in a down payment of $1500 and pays $350 per month in installments to buy a car?
• How do you define your variables when given a word problem?
• How do you write an equation of a line for Anne who wants to track the growth of the rose and finds that in the third week, the rose is 10 inches tall and in the eleventh week the rose is 14 inches tall.?
• How do you write an equation of a line if it take Andrew 20 minutes to get from a depth of 400 feet to a depth of 50 feet?
• How many pounds of corn can you buy if your total spending cash is $11.61 and tomatoes are selling for $1.29 per pound and corn is selling for $3.25 per pound and you buy 6 pounds of tomatoes?
• If the sum of three consecutive even integers is 66 what are the integers?
• If the heart of an elephant at rest will beat an average 1380 beats in 60 min, what is the rate in beats per minute?
• How do you write a linear equation that related the cost c and the number x of copies delivered if the cost to a newspaper company for sunday home delivery is approximately $0.45 per newspaper with a fixed costs of $2,080,000?
• What is the number if the sum of twice a number and 14 less than the number is the same as the difference between -26 and the number?
• How can a system of equations be used to predict media use?
• The sum of three consecutive integers is 53 more than the least of the integers, how do you find the integers?
• The sum of the three consecutive integers is 71 less than the least of the integers how do you find the integers?
• The sum of 3 consecutive integers is 108, what are the integers?
• The sum of 4 consecutive even integers is 132, what are the integers?
• The sum of three consecutive even integers is 168, what are the integers?
• Three consecutive integers have a sum of 84, what are the integers?
• The sum of two consecutive even integers is -298, what are the integers?
• One positive integer is 5 less than another. the product of the two integers is 24, what are the integers?
• If the product of two numbers is an integer, what are the integers?
• The sum of the reciprocals of two consecutive even integers is 9/40, what are the integers?
• Two consecutive integers have a product of 240, what are the integers?
• The sum of four consecutive even integers is 84, what are the integers?
• The sum of three consecutive integers is 87, what are the integers?
• The sum of two integers is 2, and their difference is 6, what are the integers?
• The sum of three consecutive integers is 915, what are the integers?
• The sum of two consecutive integers is 5, what are the integers?
• The sum of three consecutive integers is 45, what are the integers?
• The sum of three consecutive odd integers is 279, what are the integers?
• The sum of three consecutive integers is 75, what are the integers?
• The product of two consecutive positive integers is 11 more than their sum, what are the integers?
• The sum of three consecutive integers is 192, what are the integers?
• The sum of two consecutive odd integers in 112, what are the integers?
• The sum of 3 consecutive integers is 21, what are the integers?
• The sum of two consecutive odd integers is -116, what are the integers?
• The sum of three consecutive integers is 915, what are the integers?
• The sum of three consecutive integers is 36, what are the integers?
• What is the average of integers from 25 to 41?
• How do you find three consecutive integers whose sum is 42?
• How do you find 3 consecutive integers such that their sum is 27 less than three times the smallest?
• What are four consecutive even integers whose sum is 340?
• How do you find 3 consecutive odd integers where the sum is -141?
• How do you find all pairs of consecutive even integers whose sum is greater than 73 but less than 79?
• If the sum of three consecutive integers is 72, what is the second integer?
• If the sum of two consecutive integers is less than 83, how do you find the pair of integers with the greatest sum?
• The length of a rectangle is 4cm more than the width and perimeter is at least 48cm. What are the smallest possible dimensions for the rectangle?
• How do you find three consecutive integers whose sum is 171?
• How do you find three consecutive even integers whose sum is 244?
• If the sum of three consecutive even integers is 210, what are the integers?
• How do you find two consecutive odd integers whose sum is 35?
• How do you find three consecutive even integers if their sum is 36?
• How do you find two consecutive integers whose sum is 67?
• How do you find three consecutive odd integers that have a sum of 123?
• How do you find three consecutive even integers have a sum of -36?
• How do you find three consecutive odd integers?
• How do you find three consecutive odd integers such that four times the middle integer is twice the sum of the other two integers?
• For consecutive integers, the sum of the even integers is 60. What is the value of the smallest odd integer?
• If the product of two consecutive even integers is 288, how do you find the integers?
• How do you find three consecutive odd integers whose sum is 69?
• How do you find two consecutive integers such that seven times the first integer plus the second is 81?
• How do you find two consecutive odd integers such that the sum of the first and twice the second is 55?
• How do you find three consecutive even integers such that the sum of the first, third, and twice the second is -16?
• How do you find three consecutive odd integers such that when five times the third minus the second is added to the first, the result is 23?
• How do you find three consecutive integers such that the sum of their squares is 77?
• If the sum of the squares of two consecutive integers is 41, how do you find the integers?
• If the sum of two consecutive odd integers is 100, how do you find the integers?
• How do you find two consecutive integers whose sum is 73?
• If the product of two consecutive integers is 182, how do you find the integers?
• How do you find the sum of three consecutive even integers is 72?
• If the sum of three consecutive integers is 39, what are the three integers?
• If the reciprocal of the product of the two consecutive integers is 1/30 how do you find the two integers?
• If two consecutive positive integers have the property that one integer times twice the other equals 612 what is the sum of these two integers?
• If the sum of three consecutive integers is 162 how do you find the smallest integer?
• The width of a rectangle is one-fifth as much as the length and the perimeter is 120 cm, how do you find the length and width?
• The sum of a number plus half of itself is 18.75, how do you find the numbers?
• Two numbers differ by 3. The sum of their reciprocals is seven tenths. How do you find the numbers?
• The sum of two numbers is 41. One number is less than twice the other. How do you find the larger of the two numbers?
• How do you find two consecutive odd integers whose sum is 36?
• The sum of three consecutive integers is -204, what is the largest integer?
• How do you find two consecutive even integers such as that the smaller added to three times the larger gives a sum of 38?
• WhaT are 2 consecutive odd numbers that have the product of 12,099?
• The perimeter of a rectangle is 310 m. The length is 25 m greater than the width. What are the length and the width of this rectangle?
• The sum of three consecutive odd integers is 189, what are the integers?
• The sum of two consecutive even integers is 106, what are the integers?
• The sum of two consecutive even integers is 58, what is the larger integer?
• The product of two consecutive even integers is 34 less than 7 times their sum, how do you find the two integers?
• One number is 2 more than 2 times another. Their product is 2 more than 2 times their sum, how do you find the two integers?
• The sum of two consecutive integers is 17, what are the integers?
• How do you find three consecutive odd integers such that twice the sum of the three numbers is 33 or more than the third number?
• The sum of three consecutive odd integers is 177, what are the integers?
• Four consecutive even numbers have a sum of 92, what are the integers?
• The sum of 2 consecutive integers of 9, what are the integers?
• The sum of three consecutive even integers is 114, what are the integers?
• The sum of their square is 13, what are the two integers?
• The product is 30, what are the two integers?
• The square of the first added to twice the second is 5, what are the two integers?
• The product of the first and twice the second is 40, what are the two integers?
• Twice the square of the first subtracted from the square of the second is -167, what are the two integers?
• The sum of three consecutive integers is 162, what are the integers?
• Ralph bought some magazines at $4 each and some dvds at $12 each. He spent $144 and bought a total of 20 items. How many magazines and how many movies did he buy?
• I have $3.85 in my pocket in dimes and quarters only. I have three times as many dimes in my pocket as I do quarters. How many of each type of coin do I have?
• Two angles are complementary. The sum of the measures of first angle and half the measure of the second angle is 65°. How do you find the measures of the angles?
• In 2 years a boy will be 3/4 as old as his sister. 2 years ago he was 2/3 as old as she. How old are they?
• The cost of a school banquet is $65 plus $13 for each person attending. How do you determine the linear equation that models this problem and what is the cost for 81 people?
• Rose is two thirds as old as Johnny, in 5yrs the sum of their ages will be 50yrs, how do you find their present ages?
• In eight years, peter will be three times old as he was eight years ago, how old is peter now?
• A man who is 42yrs old has a son of 12yrs old in how many years will the father be twice as old as his son?
• Mr. Santos, working as a salesman for a firm, gets a salary of 5000 per month plus a commission of 10% on all sales above 2000000 per month and his total gross pay last month was 21000, how much was his total sale last month?
• Train A leaves a station 1/2 hour ahead of Train B. The trains travel on parallel tracks. Train A travels at 25km/h while train B travels at 25km/h, how many hours will it take Train B to overtake Train A?
• Mark can finish task alone in 24days while Andrei can do the same task in 18days. If they work together, how long can they finish the task?
• A variety of candies costing $10.50 per kg is mixed with another variety costing $15 per kg, to make a mixture of 12kg that would cost $12.50 per kg. how many kg of each variety were mixed?
• Three hundred people attended a band concert. Reserved seat tickets were sold at $100 each while general admission tickets cost $60 each. If the sales totaled $26000, how many tickets of each type were sold?
• Sloane brought 20 erasers and pens in total. Each pen costs $2 while each eraser costs $0.40. If he spent $32.50 in all, how many erasers did he buy?
• Kevin sweats .08 L/min when jogging at 5mph, and .18 L/min when running at 8mph. consider a linear relationship, at what speed will Kevin stop sweating?
• Your teacher is giving you a test worth 100 points containing 40 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test?
• Tasha wants 25 pounds of a nut mix that she can sell for $5.00 per pound. If she has cashews that sell for $6.50 per pound and pistachio nuts that sell for $4.00 per pound, how much of each should she use?
• The cost to a newspaper company for Sunday home delivery is approximately $0.45 per newspaper with fixed costs of $2,050,000. How do you write a linear equation that relates the cost C and the number x of copies delivered?
• A is elder to B by two years. A's father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and the sister differs by 40 years, find the age of A?
• How many liters of a 60% sugar solution should be added to 40 liters of a 30% sugar solution to produce a 50% sugar solution?
• An investment of $3000 is made at an annual simple interest rate of 5%. How much additional money must be invested at an annual simple interest rate of 9% so that the total annual interest earned is 7.5% of the total investment?
• Suppose you intend to spend $60 buying books. Hardback books cost $12 and paperback cost $5. How many books of each type can you buy?
• The annual salaries of a congressman and a senator total $288,900. If the senator makes $41,300 more than the congressman, how do you find each of their salaries?
• The length of a rectangle exceeds its breadth by 4cm. If the length is increased by 3cm and the breadth is increased by 2 cm, the new area exceeds the original area by 79 sq cm. How do you find the dimensions of the given rectangle?
• 1000 tickets were sold. Adult tickets cost $8.50, children's tickets cost $4.50, and a total of $7300 was collected. How many tickets of each kind were sold?
• A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. what is the boat's speed, and how fast does the current in the river flow?
• How do you find the cost per ounce of a mixture of 200 oz of a cologne that costs $5.50 per ounce and 500 oz of a cologne that costs $2.00 per ounce?
• A music store is selling CD's for $5.50 and $8.50. You buy 13 CDs and spend $92.50. How many $8.50 CDs did you buy?
• You are selling tickets to a concert. Student tickets cost $5 and adult cost $7. You sell 45 tickets and collect $265. How many of each type did you sell?
• When Jane's wading pool was new, it could be filled in 6 minutes, with water from a hose. Now that the pool has several leaks, it takes only 8 minutes, for all of the water to leak out of the full pool. How long does it take to fill the leaky pool?
• Milton and Bonnie are hiking. Milton averages 4 mph, and Bonnie averages 3 mph. If they start out together in the morning, but Milton gets to camp 2 hours and 30 minutes ahead of Bonnie, then how many miles did they hike that day?
• A group of sailors plans to share equally the cost and use of a $72,000 boat. If they can get 3 more sailors to join their group, the cost per person will be reduced by $2000. How many original sailors are there?
• A sum of $3000 was invested, part at 6% and the rest at 9%. How much was invested at each rate if the interest on each investment is the same?
• A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. How do you find the dimension of the room?
• A rectangular room is 6 meters longer than it is wide, and its perimeter is 32 meters. How do you find the dimension of the room?
• The sum of 3 times Darlene's age and 7 times Sharon's is 173. Darlene is 2 years less than twice as old as Sharon is. How do you find each of their ages?
• The perimeter of a rectangular carpet is 54ft. The lenght is 3ft greater than the width. How do you find the length and width?
• How do you find the total amount owed after 6 months on a loan of $900 at an annual simple interest rate of 8.5%?
• How do you estimate the tax on a $198 stereo when the sales tax is 5.25%?
• A boat salesperson earns a 2.5% commission on the sale of each boat. How do you find the commission earned on a boat that sells for $18,500?
• A cell phone distributor earns a yearly salary of $28,000 plus a 17.5% commission on sales. How do you find the total earnings for a year when the sales are $38,000?
• How do you find the simple interest paid after 3 months on a loan of $9700 borrowed at an annual interest rate of 11%?
• What are 2 consecutive odd numbers?
• What are odd numbers and prime numbers?
• What is the sum of all odd numbers between 0 and 100?
• Can you add 3 odd numbers and get an even number?
• How do you calculate the sum of odd numbers between 1 and 2001?
• How do you add all the odd numbers between 1-99 inclusive?
• What is the sum of the first 500 odd numbers?
• Is the sum of two odd numbers always odd?
• What are three consecutive odd numbers which are prime?
• What 2 odd numbers added together equal an odd number?
• Are all prime numbers odd?
• Can 5 odd numbers be added to get 30?
• Why is the product of 2 odd numbers, odd?
• What is the sum of the first 60 consecutive odd number?
• If Kate triples her height, she will be as tall as if she added 147.5 inches to half her height. How tall is Kate?
• Bob can wash a car in 6 minutes. Bill can wash a car in 8 minutes. How long will it take if Bob and Bill wash a car together?
• The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. How do you find the dimensions of the frame?
• In 15 years, Maya will be twice as old as David is now. In 15 years, David will be as old as Maya will be 10 years from now. How old are they now?
• Two bicyclists ride in opposite directions. The speed of the first bicyclist is 5miles per hour faster than the second. After 2hours they are 70miles apart. How do you find their rates?
• A speedboat drives 3 times the speed of the current. Thus, it travels downriver for 700 miles 3 hours more than it takes to travel upriver for 325 miles. How do you find the speed of the boat in still water?
• A car leaves an airport going 84 km/hr. 5 hours later, an airplane going 705 km/hr departs. How do you find the distance when the airplane will catch up with the car?
• A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How wide will the walk be?
• The measure of a supplement of an angle is 12° greater than three times the measure of a complement. How do you find the measure of the angle?
• The degrees measures of the angles of a pentagon are consecutive even integers. How do you find the measure of the largest angle?
• A rectangular garden 42 by 20 feet is surrounded by a walk way of uniform width. If the total area of the garden and walkway is 1248 square feet, what is the the width of the walkway?
• If 18 is added to a two-digit number, the digits are reversed. The sum of the digits is 8. What is the original number?
• The length of a rectangular garden is 5 less than two times the width. There is a 5 foot wide sidewalk on 2 sides that has an area of 225 sq ft. How do you find the dimensions of the garden?
• Angela math test scores so far are as follows: 87, 96, 82, 77. What score must Angela make on the final test in order to have a test average of 88?
• If you invest $1500 at a rate of 7% per year, how many years will it take to earn at least $1050 in interest?
• The measures of two angles of a triangle are 35° and 45°. What is the measure of the third angle of the triangle?
• The sum of the measures of two exterior angles of a triangle is 264 degrees. What is the measure of the third exterior angle?
• The angles of a triangle have the ratio 2:3:4. What is the measure of the smallest angle?
• Two angles of a triangle measure 30° and 50°. What is the measure of the third angle of the triangle?
• The angles of a triangle are in a ratio of 1:2:3. What is the measure of the largest angle?
• The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle?
• Two angles of a triangle measure 60, 80, what is the measure of third angle?
• If the measures of the three angles of a triangle are x, 2x-20, and 3x-10, the what is this type of triangle?
• Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle?
• If the angles of the triangle are in the ratio 3:4:5, then how do you find the ratio of the sides?
• The angles of a triangle are in the ratio of 2:3:4. What is the degree measure of the largest angle?
• If the angles of a triangle are represented by x, 3x + 20, and 6x, what kind of a triangle is it?
• If angle A is three times as large as angle B, and angles B and C sum to 90 degrees, what is the measure of each angle?
• The sum of the measures of two exterior angles of a triangle is 255. What is the measure of the third?
• How many pounds of water must be added to 40 pounds of a 10% boric acid to reduce it to a 4% solution?
• Sugar free gum contains 40% less calories than regular gum. if a piece of regular gum contains 40 calories, how many calories does a piece of sugar free gum contain?
• The sum of two consecutive odd integers is 244. What is the smaller integer?
• In a certain county, the number of Charter Schools is six less than twice the number of Alternative Schools. We know that there are 52 Charter Schools in the county. How many Alternative Schools are in the county?
• The sum of two numbers is 180 and the larger number exceeds four times the smaller number by ten, what are the 2 numbers?
• The sum of two consecutive odd integers is 236. What is the smaller integer?
• A wire is cut into 3 equal parts. the resulting segments are then cut into 4, 6, and 8 equal parts, respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire?
• Sauder has three times as much money as Sony. Sammy has $4 less than Sauder and $5 more than Sony. How much money does each have?
• How do you find the perimeter of a figure with sides 4cm, 14.56 cm, and 0.14 m?
• The width of a rectangle is fixed at 28 cm. What lengths will make the perimeter greater than 72 cm?
• How do you find the perimeter of the triangle whose vertices are these specific points on a plane (-1,6) (4,-5) (-2, -4)?
• A square has an area of 0.09 square inches. How do you find the perimeter of the square?
• How do you calculate the perimeter of a square if the area is 81?
• The perimeter of a rectangular flower garden is 60m and its area is 225 m^2. How do you find the length of the garden?
• How do you find the perimeter of an isosceles triangle whose base is 16 cm and whose height is 15 cm?
• The diagonals of a square each measure 7 feet. How do you find the area of the square?
• The sum of two numbers is 48. One number is 3 times as large as the other. What are the numbers?
• Twice the difference of a number and 8 is equal to three times the sum of the number and 3. How do you find the number?
• If 3 times a number minus 2 equals 13, what is the number?
• If the sum of a number and three is tripled, the result is nine less than twice the number, how do you find the number?
• The sum of three consecutive even integers is 42, what are the integers?
• Question #5c32b
• The store has CDs for 10 dollars, and 15 dollars. You have 55 dollars. How do you write an equation that represents the different numbers of 10 dollars, and 15 dollar CDs that you can buy?
• Over one year a company's sales increased 20% and its expenses decreased 20%. The ratio of sales to expenses at the end of that year was how many times the ratio at the beginning of that year?
• Evan purchased a boat for $8,825. He made a down payment of $2,500. He applied for a three-year installment loan with an interest rate of 10.2%. What is the total cost of the boat after three years?
• William opens a credit card with an APR of 18.63% compounded monthly. How much is charged in interest this month if his balance is $835?
• Elizabeth opened a credit card at a department store with an APR of 17.71% compounded quarterly. What is the APY on this credit card?
• Alexander has a previous balance of $982 on a credit card with a 19.2% APR compounded monthly. If he made a payment of $73 this month, what is the new balance on his credit card?
• When a number x is added to its square, the total is 12. How do you find two possible values for x?
• Suppose you are starting an office-cleaning service. You have spent $315 on equipment. To clean an office, you use $4 worth of supplies. You charge $25 per office. How many offices must you clean to break even?
• Kay spends 250 min/wk exercising. Her ratio of time spent on aerobics to time spent on weight training is 3 to 2. How many minutes per week does she spend on aerobics? How many minutes per week does she spend on weight training?
• The perimeter of a rectangular floor is 90 feet. How do you find the dimensions of the floor if the length is twice the width?
• How do you find two integers whose sum is 6 and with a difference of 4?
• If a plane can travel 576 miles with the wind in 3 hours and against the wind in 6 hours how fast is the speed of the wind?
• If 2 times the sum of 15 and a number is equal to the number divided by 4, what is the number?
• I have a number which is greater than 70 but less than 80 and is the quotient of 234. What is my number?
• It took 3 hours to row a boat 18 km against the current. The return trip with the current took 1 1/2 hours. How do you find the speed of the rowboat in still water?
• A student walks and jogs to college each day. The student averages 5 km/h walking and 9 km/h jogging. The distance from home to college is 8 km, and the student makes the trip in 1 hour. How far does the student jog?
• The length of a rectangle is 5 inches more than the width. If the perimeter is 70 inches, what is the width?
• Bob is 8 years younger than charlie. Doug is 2 years older than charlie. The sum of Charlie and Dougs ages is 4 times bobs age. How do you find the age of all boys. math problem?
• The sum of the digits of a two digit number is 9. If the digits are reversed, the new number if 63 greater than the original number. How do you find the original number.?
• Lorendo needs to run a wire from the top of a telephone pole to a stake on the ground 10 meters from the base of the pole. Does she have enough wire if the pole is 14 meters tall? If not how much does she need?
• The base of a triangle of a given area varies inversely as the height. A triangle has a base of 18cm and a height of 10cm. How do you find the height of a triangle of equal area and with base 15cm?
• The cost of a school banquet is $70 plus $15 per person attending. Determine the linear equation that models this problem. What is the cost for 44 people?
• N is a two-digit positive even integer where the sum of the digits is 3. If none of the digits are 0, what is N?
• A farmer has 3/5 of his land under cultivation, 3/4 of which is in soy beans. How much land does the farmer have if he has 270 acres of soy beans?
• The sum of twice a number and 10 is equals 180. What is the number?
• A faucet can fill a sink in 5 minutes while a drain will empty the same sink in 8 minutes. If the faucet is turned on and the drain is left open, how long will it take to fill the sink?
• Question #6367d
• Mr. Gilliam is 3 years younger than his wife. The sum of their ages is 95. How old is Mr. Gilliam?
• Broderick deposits $6,000 in an account that earns 5.5% simple interest. How long will it be before the total amount is $9,000?
• At the local grocery store, a 16-ounce bottle of apple juice costs $3.20. What is the cost of the apple juice per ounce?
• Joan's Candy Emporium is having a sale. Three pounds of gummy bunnies are selling for $4.00. How much will two pounds cost?
• A corner store sells two kinds of baked goods: cakes and pies. A cake costs $14 and a pie costs $8. In one day, the store sold 12 baked goods for a total of $144. How many cakes did they sell?
• Billy had 24 trading cards. He gave 7 of his cards to Miko and 9 of his cards to Teri. What fraction of his originai 24 cards does Billy have left?
• Giselle pays $240 in advance on her account at the athletic club. Each time she uses the club ,5$ is deducted from the account. How do you model the situation with a linear function?
• An amount of $8,000 is invested at a simple interest rate of 1.5%. What Is the total amount after 3 years?
• 5,000 people visited a book fair in the first week. The number of visitors increased by 10% in the second week. How many people visited the book fair in the second week?
• The table below shows variations in output as units of a variable factor (labour) are added to a fixed factor (capital) ?
• The difference of 9 times a number and 2 is 67, how do you find the number?
• The sum of two consecutive even integers is -34. What is the smaller integer?
• Four times the difference of 17 and a number is 84. What is the number?
• Chris made four times as many putts as Paul made at golf practice. Together, they made 60 putts. How do you find the number of putts Paul made?
• The sum of three consecutive integers is -96. What is the largest integer?
• Ky has three times more books as Grant, and Grant has 6 fewer books than Jaime. If the total combined number of books is 176, how many books does Jaime have?
• An instructor makes $15 more per hour than an assistant. If the combined hourly wage of the assistant and instructor is $65, what is the hourly wage of the assistant?
• A paralegal makes $12 more per hour than an assistant. If the combined hourly wage of the paralegal and assistant is $38, what is the hourly wage of the assistant?
• Shannon opens a savings account with $50. Each week after that she deposits $8 into her account. How many weeks does it take her to save $450?
• Ms. Patel spent $34 to buy a total of 10 packs of M&Ms and paper clips for her students. If the M&M bags were $3 and the paper clips were $4, how many of each did she buy?
• One minute is #1/60# of an hour. What part of an hour is 12 minutes?
• On a road map, the distance from Cleveland to Pittsburgh is 4.5 cm. What is the actual distance between the cities, if the map scale is 1.5 cm is 30 miles?
• At their annual car wash, the science club washes 30 cars in 45 minutes. At this rate, how many cars will they wash in 1 hour?
• How many mg of a metal containing 45% nickel must be combined with 6 mg of pure nickel to form an alloy containing 78% nickel?
• Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. How many adult tickets and student tickets were purchased?
• A pharmacist has a 10% alcohol solution and a 25% alcohol solution. How many milliliters of each solution will she need to mix together in order to have 200 mL of a 20% alcohol solution?
• Question #4491d
• On a scale drawing, #1/4# inch = #1# foot. What are the dimensions on the scale for room that is 27 feet by 20 feet?
• Question #a4968
• When the son will be as old as his father today, the sum of their ages then will be 126. When the father was as old as his son is today, the sum of their ages was 38. Find their ages?
• (i) What number exceeds its fourth root by #12#? (ii) What number exceeds its fourth root by #16#?
• The sum of three consecutive integers is #-114#. What are the three integers?
• How do you trisect an angle?
• Item A costs 15% more than item B. Item B costs 0.5€ more then item C. All 3 items (A, B and C) together cost 5.8€. How much does item A cost?
• Train A got from one city to another 45min faster than train B. Train's A speed is 48km/h, train's B speed is 36km/h. What is the distance between the cities?
• Arnold puts a $139.00 coat on layaway. He is required to make a 25% deposit. How much will Arnold pay later to get his coat out of layaway?
• There were 110 books in two bookshelves. If we put half of the books from bookshelf B to bookshelf A, then there will be four times more books in bookshelf A, than there is now in bookshelf B. How many books were in the bookshelves in the beginning?
• Question #e769e
• Question #2da35
• Question #ffc84
• What are some real life uses of Boolean logic?
• Question #51881
• Billy needs to read 500 minutes this week for his English class. He is going to read 6 days. If he already reads 15 minutes every day, how many additional minutes does he need each day to read at least 500 minutes?
• Question #a1ad0
• Here are the numbers of pages in the books on a reading list. 71 96 110 112 114 114 121 127 135 175 180 Which data values are outliers? Choose all answers that are correct.
• Papa is putting new concrete on a driveway. The driveway is 30' x 10' x 9" thick. Concrete is measured by the cubic yard. One sack of dry cement mix costs $7.30, and it takes four sacks to mix up 1 cubic yard of concrete. How much will it cost?
• Question #85ba3
• Question #a920f
• Question #f8974
• Question #ce087
• Question #3a28b
• Question #0a9ed
• Father bought 3 cakes at $7.90 each , 6 hot dogs at $1.05 each and some icicles at $0.50 each . the ttoal amount that father paid was $39.50, how many icicles did he buy?
• If 3 times the smaller of 2 consecutive integers is added to 4 times the larger, the result is 102. find the smaller?
• What are real world applications of power series ?
• Question #c3149
• A drawing of a property is to the scale of 0.5 inches to 6 feet. If a wall is 30 feet long what would its length be on the drawing?
• The length of a rectangular garden is 7 m greater than the width. the area is 78m^2. what are the dimensions for length and width?
• Question #f1ddd
• Question #c52ba
• If ratio of AM and GM of two numbers is #5/4#, what are the numbers and what is their HM?
• Question #590ae
• Question #e2cba
• What is the sum of the measures of the interior angles of an octagon?
• Enter the measure of an exterior angle of a regular pentagon?
• A vacuum cleaner uses #5/8# kilowatts per hour. A clothes dryer uses #4 11/16# kilowatts per hour. How many hours can the vacuum run and use the same amount of energy as the clothes dryer does in one hour?
• Question #44793
• Question #c5d4c
• Question #e682a
• Question #94595
• Question #d3c60
• Question #c5884
• Dominic earns $285 per week plus an 8% mission rate on all his sales. If Dominic sells $4,213 worth of merchandise in one week, how much will his total earnings for the week be?
• Adita earns $9.40 per hour working at an animal shelter. How much money will she earn for 18.5 hours of work?
• Halima is now three years older than Nekesa If Nekesa's age is represented by #x#, what will be the sum of their ages in 10 years time?
• Which of the following numbers is not the sum of three consecutive integers: 51, 61, 72, 81?
• The length of a rectangle is 8 cm greater than the width. The area of the rectangle is 105 cm 2. How do you find the width and the length?
• Question #00ba1
• Fingernails grow about 1.5 inches per year. How long would it take to grow nails 37 inches long?
• Question #66f05
• You have the choice of accepting one of two jobs. The first job pays a $200 weekly base salary and 15% of all sales. The second job pays a $300 weekly base salary and 10% of all sales. How much sales do you need for both jobs to pay the same?
• Question #25a29
• The sum of two numbers is 19 and their difference is 3. What are the two numbers?
• Question #ab60e
• Jason bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 42 cards left. How many cards did Jason start with?
• Question #cf87c
• Florida's coastline is 118 miles shorter than four times the coastline of Texas. It is also 983 miles longer than the coastline of Texas. What are the lengths of the coastlines of Florida and Texas?
• Question #7a122
• Question #24690
• Question #32a4f
• If #a/(b+c) + b/(c+a) + c/(a+b)=1# prove that #a^2/(b+c) + b^2/(c+a) + c^2/(a+b)=0# ?
• The geometric mean of two numbers is 8 and their harmonic mean is 6.4. What are the numbers?
• Let #S_n = n^2 + 20n + 12, n# is a positive integer. What is the sum of all the possible values of #n# for which #S_n# is a perfect square?
• Question #75b7f
• Question #9c419
• Sydney, Australia is 13 hours ahead of my current location. If it's 3:00 pm here, what time is it in Sydney, Australia?
• Question #6ce72
• Dad is 10 years older than his three sons ages combined. In how many years will dad's age be same as ages of his sons combined?
• Question #21d4a
• Question #24c58
• Question #7d037
• How do you solve this?
• Question #65e4f
• Question #e3fc9
• If the sum of three consecutive integers is #81# then what are the three integers?
• Question #c6b2b
• Question #64251
• Question #46578
• What is largest #4#-digit number which can be formed with the digits #1,9,6,4#?
• How many possible sets of three odd numbers are there whose sum is even?
• Question #2d9fe
• Question #10e8c
• Squares of side #3# inches are cut from each corner of a square sheet of paper. The paper is folded to form an open box with a volume of #675# cu in. How long were the sides of the sheet of paper?
• Twice the difference of a number and 8 is equal to three times the sum of the number and 4. What is the number?
• If #x+y=19# and #xy=78#, find #y-x#?
• Question #9bd0f
• Suppose you have two bags, A and B, with a total weight of 27 pounds, and you know that bag B weighs 3 pounds more that twice as much as A. How much do each of the bags weigh?
• Question #7abdc
• Question #eae6b
• How to construct linear equations Q2b) Q11 and Q13?
• Question #e3e9e
• How to construct linear model?
• Construct an equation that models the repayment of a high value loan. Such as a mortgage. The loan is based on compound interest with a monthly calculation and repayment cycle. The site system forcing me to add a question mark: ?
• Question #aff76
• Question #b0b47
• Summer and Jason's present ages add up to #107# years. If #11# years ago Jason's age was four times Summer's age, how old is Jason now?
• Prove that #if n# is odd, then #n=4k+1# for some #k in ZZ# or #n=4k+3# for some #k in ZZ#?
• There is a two digit number where the sum of the digits is 7. The actual value of the number is such that it equals 12 times the first digit minus 2. What is the number?
• When one-half of a number is added to one-seventh of the number, the sum is 27. What is the number?
• Aidan is #18# years older than Summer. If he is #46# now, when was he twice her age?
• Question #38d90
• How do you prove #(a o+ b) o+ (~ a & ~ b) = 1# ?
• Question #eb036
• Question #f0641
• Question #299fa
• What is #(x+1)+(x-2)+(x+3)+(x-4)+...+(x+99)+(x-100)# ?
• Give a real life situation problem which is mathematically translated into #2x+y+2z=18#?
• Question #bbf39
• Question #be0a3
• How do you find two numbers which differ by 5, such that twice the first number less three times the second will give an answer of #2#?
• Question #8beb6
• Question #d14f7
• The sum of two numbers is 8 and the sum of their squares is 32. What is the smaller number?
• What number is midway between 1/2 and 1?
• Show that the product of two consecutive even numbers is divisible by #8# ?
• Question #47bbb
• Question #4c7d3
• Question #92422
• Question #c086b
• What is the missing number?
• Question #254f8
• How do we add two numbers using logic gates?
• A farmer has 300 feet of fencing and wants to enclose a rectangular corral that borders his barn on one side and then divide it into two plots with a fence parallel to one of the sides. ?
• Joe flies a plane 300 miles in 2 hours to a destination with the wind. On the return trip against the wind, he only flies 270 miles in 2 hours. Assuming wind speed is constant, what's the wind speed?
• Question #303eb
• A piece of rope 20 feet long is cut from a longer piece that is at least 32 feet long. The remainder is cut into four pieces of equal length. How would you describe the length of each of the four pieces?
• James has 33 coins in his pocket, all of them nickels and quarters. If he has a total of $2.25, how many quarters does he have?
• A club sells tickets to a event for $8 for children and $10 for adults. If they sold 220 tickets and the total amount received from tickets sales was $2030, how many children tickets and how many adult tickets were sold?
• Question #27605
• Emilio has 189 books to put onto 9 shelves. Some shelves hold 15 books and others hold two dozen. How many of each size shelf will Emilio use?
• If sum of six consecutive integers is #393#, what is the third integer?
• Over five weeks, you earned a total of $1,472.50. You were paid $7.75 per hour and worked the same number of hours each week. How many hours per week did you work?
• If 6 books cost £18, how much would 7 books cost?
• Toni, Bianca, and Gemma have three consecutive whole numbers of dollars. The total amount of money they have is $66. How much money does each person have?
• Question #5db8f
• A store sells bicycles for $250 each. In one week, the store had $1,250 in bicycle sales. How many bicycles did the store sell?
• If # 3a + 1= \frac { 13} { 3}#, what is the value of #3a - 3#?
• Jane has scored the following marks on the first #5# exams: #65, 70, 55, 87, 87.# What is the minimum score she must achieve on the last exam if she is to reach her target of a #70%# average?
• Question #824dd
• Question: If 1/2 of 5 is 3, then what is 1/3 of 10?
• A Mighty Kids meal includes 3.2 ounces of applesauce. If a child eats two frozen meals each week, how many ounces of applesauce will they consume in one year?
• Question #b8408
• Question #424e2
• Question #334b6
• How would I solve this?ASB sells tickets to a dance for $10 to students who have an ASB sticker and $12 to those who don't have an ASB sticker. 160 tickets are sold and $1720 is raised. How many of each are sold?
• A principal is choosing between two field trips. The first costs $800. The second costs $240 plus $40 per student. For what number of students is the first trip less expensive?
• Question #ff015
• A shopkeeper orders 1000 pencils at $.23 each. How much does the shopkeeper pay in total?
• What is #9 xx 7 = #?
• How much baseboard is needed to go around a rectangular room that measures #18# feet by #13# feet. If baseboard costs #$1.87# per foot, what is the total cost needed for materials?
• Four less than the product of a number and 8 is twice the sum of the number and 10. What is the number?
• A bag of grapes is being divided into 24 smaller bags of 4 ounces each for snacks during a field trip. What is the division equation to find the number of ounces in the larger bag?
• Question #57ab3
• What is 1 week 5 days 14 hours plus 2 weeks 6 days 10 hours?
• Bo earns $8.95 per hour plus commission. Last week, he worked 32.5 hours and earned $28.75 in commission. How much money did Bo earn last week?
• Holly's grandfather is 52 years older than her. In 7 years, the sum of their ages will be 70. What is Holly's present age?
• Question #30cf8
• Thirty-two cyclists make a seven-day trip. Each cyclist requires 8.33 kilograms of food for the entire trip. If each cyclist wants to eat an equal amount of food each day, how many kilograms of food will the group be carrying at the end of Day 5?
• 105 students were divided equally into 15 teams. a. How many players were on each team? b. If each team had 3 girls, how many boys were there altogether?
• The admission prices for a small fair are $1.50 for children and $4.00 for adults. In one day there was $5050 collected. If we know that 2100 children paid admission, how many adults paid admission?
• A bucket holds 5 gallons and 3 quarts. What is the bucket's capacity in quarts?
• Question #bab68
• Angela bought apples and bananas at the fruit stand. She bought 20 pieces of fruit and spent $11.50. Apples cost $.50 and bananas cost $.75 each. How many of each did she buy?
• The price of a box of 15 cloud markers is $12.70. The price of a box of 42 cloud markers is $31.60. All prices are without tax, and the price of the boxes is the same. How much would 50 cloud markers in a box cost?
• Ben was walking in Manhattan at a constant speed. He went along 5th avenue from 4th to 98th street. At 3:00 he was on 15th street, and at 4:30 he was on 45th street. When did he start and when did he finish his walk?
• A total of 432 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
• Edwards mother in 57 years old her age 3 years more than twice Edwards what is Edwards age?
• 3 odd consecutive numbers have a sum of 75. What is the greatest number?
• Amber coaches soccer and volleyball. She coaches both sports for a total of 7 hours each day. The soccer practice lasts 1 hour more than twice as long as the volleyball practice?
• Adam works part time at a fast food restaurant that pay $x per hour while jenny works as a sales assistant in boutique that pays $(X+2) per hour Adam work 8 hour more per week than Jeeny and they each earn $192 a week . find the value of x and the number?
• If 12 friends want 1/3 of a sandwich each how many sandwiches would they need to order?
• Large Marbles cost 25 cent and small marbles cost 10 cents. Sally buys 18 marbles for a total cost of 2.85. How many large marbles does she buy?
• The sum of two numbers is 15. One number is twice as large as the second number. What are the two numbers? Which let statement would you use?
• The sum of two consecutive even numbers is 38. What is the larger number?