The sum of two numbers is 57, and their difference is 27. What are the two numbers?

Answer: x = 32, y = 25

Step-by-step explanation:

You can write 2 equations that meet the criteria:

The sum of two numbers is 57

x + y = 57

The difference is 7

x - y = 7

Solve the second equation for x, and substitute in the first equation to solve for y

- solve the second equation for x.

Add y to both sides of the equation

x - y + y = 7 + y

x = 7 + y

- substitute x = 7 + y into the first equation

x + y = 57

(7 + y) + y = 57

7 + 2y = 57

Subtract 7 from both sides of the equation

7 - 7 + 2y = 57 - 7

2y = 50

Divide both sides of the equation by 2 to solve for y

y=25

Insert y = 25 into either equation and solve for x

x - y = 7

x - 25 = 7

Add 25 to both sides of the equation

x - 25 + 25 = 7 + 25

x = 32

Answer: x = 32, y = 25

As a check, plug these values into both equations to make sure that it works