Mixture Problems

Key Questions

• How do you create your equations when working on a mixture word problem?

  Let's try to think about the general form of a word problem involving mixtures.

  In general, we have the following scenario:

  • a merchant sells two kinds of products (coffee, sweets, etc).

  • we know the unit prices for both kinds of products and for the final mixture
    #p_1# US dollars per pound for the first kind of product,
    #p_2# US dollars per pound for the second kind of product
    #p_m# US dollars per pound for the mixture

  • we know the total quantity formed by the mixture of the two products (#q# pounds)

  • we have to find out the quantities of each product needed to form the mixture
    (here we have the variables: #x# denoting the quantity of the first kind of product and #y# denoting the quantity of the second kind of product)

  Now, we have sufficient information to work out the equations.

  First, we know that the sum of the two quantities is #q# pounds, which gives us the first equation:
  #x+y=q#

  Second, we know that the sale price is the product of quantity and unit price, which gives us the second equation:
  #p_1 x + p_2 y = p_m*q#

  Now, we have a system of two linear equations that can be easily solved by substitution.

  Alex Boroda · 1 · May 27 2015
• What are commonly used mixture problem examples?

  For mixture problems, the problems usually (but not always) deal with solutions.

  When dealing with mixture problems, you need equate the amount of the compound

  ---

  Here are some examples

  • Heating the solution so that some of the water will evaporate and the solution will become more concentrated. Usually, when evaporation is involved, the assumption is that only the water evaporates

  Example:
  Heating a 500 mL 40% alcohol solution such that the resulting alcohol solution will become a 70% alcohol solution

  #(0.40)(500) - (0.00)(X) = (0.70)(500 - X)#

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  • Mixing the solution with the pure form of the compound to increase the concentration

  Example:
  Mixing a 500 mL 40% alcohol solution with pure alcohol such that the resulting alcohol solution will become a 70% alcohol solution

  #(0.40)(500) + (1.00)(X) = (0.70)(500 + X)#

  ---

  • Diluting the solution with water so that the solution will become less concentrated

  Example:
  Diluting a 500 mL 70% alcohol solution with water such that the resulting alcohol solution will become a 40% alcohol solution

  #(0.70)(500) + (0.00)(X) = (0.40)(500 + X)#

  ---

  • Mixing two different concentrations of solution so that the resulting solution will have a concentration that is somewhere in the middle of the two solutions

  Example:
  Mixing a 500 mL 70% alcohol solution with 40% alcohol solution such that the resulting alcohol solution will become a 50% alcohol solution

  #(0.70)(500) + (0.40)(X) = (0.50)(500 + X)#

  seph · 1 · Nov 4 2014
• How do you solve mixture problems using system of equations?

  Just to make it easier for me, I usually make a small table with the headings "Components", "Unit Value", "Amount" and "Value".

  Consider the following question:

  How many pints of 20% acid solution and 70% acid solution must be mixed to obtain 40 pints of 50% acid solution?

  First, I'll set up my table. I'll fill in the unknowns with variables #x# and #y#.

  

  From this, we can easily set up the two equations.

  Sum of values of two acids = Value of mixture

  Therefore, #0.20x + 0.70y = 20#

  For convenience, we'll multiply the entire equation by 10,

  #2x + 7y=200#

  This is equation (1)

  Setting up the second equation,

  Sum of amounts of each acid = Amount of mixture

  #x+y=40#

  To make at least one term of this equation identical to a term of equation (1), we'll multiply the entire equation by 2,

  #2x+2y=80#

  This is equation (2)

  Subtracting equation (2) from (1),

  #(+) 2x + 7y=200#
  #(-)2x+2y=80#
  #--------#
  #(=)0+5y=120#

  Thus,
  #5y=120#

  #y=120/5=24#

  Substituting #y=24# in (2),

  #2x+2(24)=80#
  #2x+48=80#
  #2x=80-48=32#
  #x=32/2=16#

  So, we have
  #x=16# and #y=24#

  We can conclude that 16 pints of 20% acid solution must be mixed with 24 pints of 70% solution to obtain 40 pints of 50% solution.

  ---

  I hope your question was answered.

  Tanish J. · 3 · Nov 26 2014

• How do you solve mixture problems using system of equations?
• How do you create your equations when working on a mixture word problem?
• What are commonly used mixture problem examples?
• How many pounds of each should I buy if I have $15.00 and wish to buy five pounds of mixed nuts for a party where peanuts cost $2.20 per pound and cashews cost $4.70 per pound?
• How many liters of each should be mixed to give the acid needed for the experiment if it calls for one liter of sulfuric acid at a 15% concentration, but the supply room only stocks sulfuric acid in concentrations of 10% and 35%?
• How much of each type should a farmer mix to obtain 100 liters of fertilizer in a 12% solution if he has fertilizer in 5% and 15% solutions?
• How many of each coin does Nadia have if she empties her purse and finds that it contains only nickels and dimes, has a total of 7 coins and they have a combined value of 55 cents?
• Lisa will make punch that is 25% fruit juice by adding pure fruit juice to a 2-liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add?
• How much of each chemical is needed to make 750 kg of the plant food, if a plant food is to be made from three chemicals and the mix must include 60% of the first and second chemicals, the second and third chemicals must be in a ratio of 4 to 3 by weight?
• Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she have?
• A 5-lb nut mixture is worth $2.80 per pound. The mixture contains peanuts worth $1.70 per pound and cashews worth $4.55 per pound. How many pounds of each type of nut are int he mixture?
• A chemist needs to create a 25% citrus mixture by adding 20 mL of a 80% citrus solution to a 5% citrus solution. How much of each is needed?
• A chemist is making a solution that is to be 55% chlorine. He has one solution that is 40% chlorine and another that is 65% chlorine. He wants 100 liters of the final solution. How much of each should he mix?
• The Nut Barn needs 10 pounds of mixed peanuts and cashews to sell for $8.50 per pound. Cashews alone sell for $10 per pound and peanuts for $7.50 per pound. What is the amount of cashews that can be in the mixture and hold the price to $8.50 per pound?
• There were 80 people at a play. Admission was 40$ for children and 60$ for adults. The receipts amounted to 3,800$. How many adults and children attended the play?
• You have a total of 25 coins consisting of 10 and 5 cents. The total value is 3.85. How do you find the number of 10 centavo coins and 5 centavo coins?
• A student accidentally poured 2 liters of 20% acid solution into a container having 10 liters of 15% acid solution. What is the concentration of the new solution?
• A man invested some amount at 6% interest rate and some amount at 9% interest rate. If he put Php12,000 more in the second investment than in the first investment and his annual income from both investments is Php4,830 how much did he invest at each rate?
• A grocer wishes to blend 2 different coffee brands. he wants to make a blend of 480 pounds to sell at $2.68 a pound. if he uses a blend of coffee worth $2.50 a pound with another blend worth $2.80 a pound, how many pounds of each does he use?
• How many ounces of iodine worth 30 cents an ounce must be mixed with 50 ounces of iodine worth 18 cents an ounce so that the mixture can be sold for 20 cents an ounce?
• Candy A sells for $2.50/kg. Candy B sells for $5.00/kg. What quantities of each kind of candy should be used to make up a 100 kg mixture to sell for $4.00/kg?
• A solution contains 25% copper sulphate. Another solution contains 50% copper sulphate. How much of each solution should be used to make 1000 mL of a solution that's 45% copper sulphate?
• A pasture is twice as big as it is wide. Its area is 115,200 ft^2. How wide is the pasture?
• How many pounds of dried pineapple selling at 35 cents a pound should be mixed with dried apricots selling at 70 cents a pound to make a mixture of 100 pounds to sell at 42 cents per pound?
• How much salt must be added to 800 grams of a solution that is 15% to obtain a solution that is 20% salt?
• A chemist mixes a 200 L of a solution that is 60% acid with a 300 L of a solution that is 20% acid. What is the percentage of the mixture?
• How much water must be added to 20 L of a 10% solution of boric acid to reduce it to a 4% solution?
• How many grams of water must be evaporated from 100 kilograms of a 40% salt solution to produce a 50% salt solution?
• A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 L of a solution containingg 42% insecticide. How much of each solution should be used?
• How many liters of water must be added to 8 liters of a 40% acid solution to obtain a 10% acid solution?
• How much water must be added to 12 grams of a 90% iodine solution to produce a 25% iodine solution?
• Maria can build a model train in 7 hours. Anne can build a model train in 5 hours. How long would it take them if they work together?
• A gardener has 26 lb. of a mixture of fertilizer and weed killer. If 1 lb. of the mixture is replaced by weed killer, the result is 5% weed killer. What % of the original mixture was the weed killer?
• A health food store sells trail mix made with granola and dried fruit. The store buys granola at $1.00/lb and dried fruit at $2.00/lb, and it sells these items at 25% markup. If the trail mix sells for $1.75/lb, what is the recipe for trail mix?
• How many gallons of 4% milk should you mix with 1% milk to make 10 gallons of 3% milk?
• How many gallons of a 15% acid solution must be mixed with 5 gallons of a 20% acid solution to make a 16% acid solution?
• Copper that was 95% pure was melted together with copper that was 75% pure to make 15 kilograms of an alloy that was 83% pure. How many kilograms of each kind were used?
• A Merchant muxed 30lbs of peanuts with 20lbs of cashews. The 50lbs mixture sells for $203. A second mixture included 40lbs of peanuts and 60lbs cashews. The 100 lb mixture sells for $484. How do you find the cost per pound of the cashews?
• How much of a 75% copper alloy should be melted into 62 kg of a 35% copper alloy to produce an alloy which is 50% of copper?
• A nurseryman is preparing an insecticide by mixing a 95% solution with water (0% solution). How much solution and how much water are needed to fill a 100 L tank with 3.8% solution?
• Suppose a fuel mixture is 5% ethanol and 95% gasoline. How much ethanol (in gallons) must you add to one gallon of the fuel so that the new fuel mixture is 10% ethanol?
• How many quarts of milk containing 4% butter fat and how many quarts of cream containing 29% butter fat must be mixed to make 40 quarts of cream containing 20% butter fat?
• How many quarts of a solution half of which is acid must be added to 10 quarts of a solution one-fifth of which is acid to from a solution which is three-tenths acid?
• A custodian is going to mix a 4% ammonia solution and a 12% ammonia solution to get 1 gallon (128 fluid ounces) of a 9% ammonia solution. How many fluid ounces of the 4% solution and the 12% solution should be used?
• A grocer wishes to mix some nuts worth 90 cents per pound with some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.30 per pound. How much of each should she use?
• Cashews at $7.40 a pound are mixed with peanuts at $2.60 a pound. If there are 18 pounds in the mixture and the mixture sells for $5.80 per pound, how many pounds of cashews are there in the mixture?
• A store manager has 50 pounds of coffee which sells for $10 per pound. How much coffee worth $6 per pound must she mix with it so that she can sell the mixture for $8.5 per pound?
• A grocer has two kinds of nuts, one that costs $5.00 per kilogram and another that costs $5.40 per kilogram. How many kilograms of each type of nut should be mixed in order to have 40 kg of a mixture worth $5.25 per kilogram?
• How many pounds of peanuts that cost $0.70 per pound and cashews that cost $0.90 per pound can be combined to make 300 pounds of a mixture that will sell $0.75 per pound?
• If an alloy containing 30% zinc is mixed with a 55 % zinc alloy to get 800 pounds of 40% alloy, how much of each must be used?
• How many liters each of 15% acid and 33% acid should be mixed to get 120 L of 21% acid?
• How do you find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 60 quarts of 2% butterfat milk?
• Sharon has two solutions available in the lab, one solution with 6% alcohol and another with 11% alcohol. How much of each should she mix together to obtain 10 gallons of a solution that contains 7% alcohol?
• A merchant has 5 pounds of mixed nuts that cost $30. He wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. How many pounds of peanuts are needed?
• Your chemistry professor gives you a 5 gallon jar containing 2 gallons of 40% alcohol. He asks you to reduce the concentration to 25%. How much water must you add to the jar?
• How many kg of pure salt must be added to 8 kg of a 30% solution to obtain a 35% solution?
• Two friends are painting a living room. Ken can paint it in 6 hours working alone. If Barbie works alone, it will take her 8 hours. How long will it take working together?
• Duk Son wants to mix 20% saline solution with a 12% saline solution to make 40 ounces of a solution that is 15% saline. how many ounces of the 12% saline solution will he need?
• The car needs 40 liters of 40% of antifreeze now it has 40 liters of 20% antifreeze how many liters need to be drained and replaced to get the desired strength?
• A plant food is to be made from 3 chemicals. The mix must include 60% of the first and second chemicals. The second and third chemicals must be in the ratio of 4:3 by weight. How much of each chemical is needed to make 750kg of the plant food?
• A nurse has two solutions that contain different concentrations of a certain medication. One is a 30% concentration and the other is a 15% concentration. How many cubic centimeters of each should she mix to obtain 45 cc of a 20% solution?
• How many pounds of gourmet candy selling for $2.20 per pound should be mixed with 6 pounds of gourmet candy selling for $1.20 per pound to obtain a mixture selling for $1.60 per pound?
• Lucy has 34 coins consisting of nickels and quarters amounting to $2.90. How many coins of each kind does she have?
• Tickets for a concert were priced at $8 for students and $10 for nonstudents. There were 1210 tickets sold for a total of $11,700. How many student tickets were sold?
• An executive is earning $51,000 per year. This is $13,000 less than twice her salary 4 years ago. How do you find her salary 4 years ago?
• Raoul received a $25 tip for waiting on a large party. This was $10 more than one-fourth of the tip the headwaiter received. How much did the headwaiter get for a tip?
• The rainfall in June was 11.6 inches. This was 2 in. less than twice the rainfall in July. How do you find the amount of rainfall in inches for July?
• You are preparing tarts. Each tart shell consists of 3 ounces of flour. lf you prepare 40 tarts, how many pounds of flour do you need?
• A vinegar-water solution is used to wash windows. If 1200L of a 28% solution are required, but only 16% and 36% solutions are available, how much of each should be mixed?
• Soybeal meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240 lb mixture that is 10% protein?
• A mixture of 30 liters of paint is 25% red tint, 30% yellow tint and 45% water. Six liters of red tint are added to the original mixture. What is the percent of red tint in the new mixture?
• How much water must be added to 200 gallons of mixture which is 80 percent alcohol to reduce it to a 75 percent mixture?
• Chocolates costing $8 per pound are to be mixed with chocolates costing $3 per pound to make a 20 pound mixture. If the mixture is to sell for $5 per pound, how many pounds of each chocolate should be used?
• A chemist wants to make 3 liters of a 7% acid solution by mixing a 9% acid solution and a 4 percent acid solution. How many liters of each solution should the chemist use?
• How many liters of a 7% solution of salt should be added to a 27% solution in order to obtain 640 liters of a 12% solution?
• Crane A can unload a ship in 10 hours and crane B can unload it in 14 hours. How long will it take the two cranes to unload the ship working together?
• It takes John 20 hours to paint a building. It takes Sam 15 hours to paint the same building. How long will it take for them to paint the building if they work together, with Sam starting one hour later than John?
• How much water must be added to 12 L (liters) of a 40% solution of alcohol to obtain a 30% solution?
• How much pure antifreeze must be added to 12 L of a 40% solution to obtain a 60% solution?
• A health food store sells oatmeal for $3.60 per pound and bran flakes for $4.80 per pound. How many pounds of each should be used to get a mixture of 30 pounds that sells for $4.00 a pound?
• Arnold needs a 25% solution of nitric acid. He has 20 milliliters (ml) of a 30% solution. How many ml of a 15% solution should he add to obtain the required 25% solution?
• A chemist mixes a 10% saline solution with a 20% saline solution to make 500 milliliters of a 16% saline solution. How many milliliters of each solution does the chemist mix together?
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• A metal alloy consists of aluminum, copper and tin mixed into a ratio of 7:5:3. How much of each metal is there in 450 g of the alloy?
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• 9 oz of Ted's special coffee blend was made by combining 3 oz of brand X coffee which costs $6/oz with 6 oz of brand Y coffee which costs $12/oz. What is the cost per oz of the mixture?
• Julio and Jake start their reading assignments the same day. Jake is reading a 168-page book at a rate of 24 pages per day. Julio's book is 180 pages long and his reading rate is 11 times Jake's rate. After 5 days, who will have more pages left to read?
• How many kg of mixed nuts that contain 40% peanuts must Jenny add to 6 kg of mixed nuts that contain 30% peanuts to make a mixture with 34% peanuts?
• The owner of Snack Shack mixes cashews worth $5.75 a pound with peanuts worth $2.30 a pound to get a half-pound, mixed-nut bag worth $1.90, How much of each kind of nut is included in the mixed bag?
• Chocolates costing $8 per pound are to be mixed with chocolates costing $3 per pound to make a 20 pound mixture. If the mixture is to sell for $5 per pound, how many pounds of each chocolate should be used?
• A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90 cents a pound. How many pounds of the $1.50 chocolate were used to make the mixture?
• Rosamaria is setting up a 20-gallon saltwater fish tank that needs to have a salt content of 3.5%. If Rosamaria has water that has 2.5% salt and water that has 3.7% salt, how many gallons of the water with 3.7% salt content should Rosamaria use?
• Harold bought 3 pounds of red apples and 42 pounds of green apples from Blue Star Grocery, where both kinds of apples are s17s a pound. How much did Harold spend on apples?
• A radiator contains 10 quarts of 30% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture 40% antitreeze?
• A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used?
• How do you find how many quarts of 5% butterfat milk and 2% butterfat milk should be mixed to yield 45 quarts of 4% butterfat milk?
• A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90 cents a pound. How many pounds of the $1.50 chocolate were used to make the mixture?
• How much 25% antifreeze and 50% antifreeze should be combined to give 40 gallons of 30% antifreeze?
• A candy store merchant sells 25 kg of ju-jubes for $3.00/kg. If he uses one brand selling for $2.25/kg and a second brand selling at $3.75/kg, how much of each brand is required?
• At a fair, 500 pounds of mixed candy was sold for $192.50. If part of the candy was candy corn and was worth $0.35 per pound and the other part of the candy was candy pumpkins worth $0.40 per pound, how many pounds of each were in the mixture?
• Keil is going to make 13 pounds of mixed nuts for a party, Peanuts cost $3.00 per pound and fancy nuts cost $6.00 per pound. If Keil can spend $63.00 on nuts, how many pounds of each should he buy?
• How much pure acid should be mixed with 5 gallons of a 20% acid solution in order to get a 50% acid solution?
• Sean wants to make a mixture that is 50% lemon juice and 50% lime juice. How much lemon juice should he add to a juice that is 30% lemon juice and 70% lime juice to make 7 gallons 100% of the 50% lemon/50% lime juice mixture?
• If it takes two roofers 4 hours to put a new roof on a portable classroom. If the first roofer can do the job by himself in 12 hours, how many hours will second roofer to do the job by himself?
• Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. lf the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?
• One canned juice drink is 15% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 10 L that is 14% orange juice?
• Soybean meal is 16% protein; commealis 8% protein. How many pounds of each should be mixed together in order to get 320-b mixture that is 14% protein. How many pounds of the cornmeal should be in the mixture?
• Soybean meal is 12% protein, cornmeal is 6%protein. How many pounds of each should be mixed together in order to get 240-b mixture that is 7% protein? How many pounds of the cornmeal should be in the mixture?
• Sue, an experienced shipping clerk, can fill a certain order in 9 hours. Felipe, a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order?
• One canned juice drink is 20% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice?
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• We want to create 50 liters of 45% concentrated acid. We have two solutions - one is 30% acid and the other is 60% acid. How much of each is needed to create our desired solution?
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• A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chef wants to make 200 mL of a dressing that is 11% vinegar. How much of each brand should she use?
• If #20# quarts of milk contains #2# quarts of butter fat, how much pure water would be need to be added to the milk to make it #4%# butter fat?
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• A chemist has a solution that is 20% hydrochloric acid (hcl) and a solution that is 50% hcl. how much of each solution should be mixed to obtain 300 cubic centimeters (cc) of a solution that is 30% hcl?
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• How many gallons of 3% acid solution must be mixed with 60 gallons of 10% acid solution to obtain an acid solution that is 8%?
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• A team of 10 people made 1200m long in 3 days. If the team has 15 people have to make 2400m,how many day they need to finish work?
• How many cup of juice must be added to 30 cup of punch that is 8% grapefruit juice, to obtain a punch that is 10% grapefruit?