I need help on finding a sum of 2 numbers that adds up to 186. The difference between them is 32, can you help me?

2 Answers
May 25, 2018

77 and 109

Explanation:

With two unknowns it is necessary to have two equations.

Let x = one number
Let y = the other number

x + y = 186x+y=186
x-y = 32 xy=32

Solve the second equation for x

x - y + y = 32 + y xy+y=32+y This gives a value for x

x = 32 + y x=32+y Put this value into the first equation

32 + y + y = 186 32+y+y=186 Solve this equation for y

32 + 2y = 186 32+2y=186 subtract 32 from both sides

32- 32 + 2y = 186 - 32 3232+2y=18632 this gives

2y = 154 2y=154 divide both sides by 2

# 2y /2 = 154/2 so

y = 77y=77

Put this value in for the second equation for x

x = 77 + 32x=77+32

x = 109 x=109

May 25, 2018

x = 109x=109

y = 77y=77

General steps are in bold.

Explanation:

Make two equations. Let xx represent the first number and yy represent the second number.

First equation: The sum of two numbers adds up to 186186:

color(red)(x + y = 186)x+y=186

Second equation: The difference between the two numbers is 3232:

color(green)(x - y = 32)xy=32

Now you can solve for one of the variables by taking either equation. I will use the first equation to solve for xx.

color(red)(x + y = 186)x+y=186

color(white)(.....)color(orange)(x = 186 - y)

Since you now know what x is equal to, you can sub it into the second equation then solve for y.

color(white)(............)color(green)(x - y = 32)

sub in color(orange)(x = 186 - y)

(color(orange)(186 - y)) - y = 32

color(white)(.......)186 - 2y = 32

color(white)(.............)-2y = 32 - 186

color(white)(.............)-2y = - 154

color(white)(...................)y = 77

Now you have the y value. You can sub this into either equation to find the x value. I will use the first equation.

color(white)(.)color(red)(x + y = 186)

sub in y = 77

x + 77 = 186

color(white)(........)x = 109

Therefore the two numbers are 109 and 77.