Question

The sum of two numbers is 58 and the difference is 20. What are the numbers?

Larger number:
Smaller number:

Answer 1

Larger number: 39

Smaller number: 19

Explanation:

Write two equations and solve the system of equations.

One number can be x. The other number can be y.

"sum" means adding.

x + y = 58

"difference" means subtracting.

x - y = 20

Take both equations, stack them and add them together from the top down.

x + y = 58

x - y = 20

_________

2x = 78

Divide by 2

x = 39

Use either original equation to find the other number.

x + y = 58

39 + y = 58

subtract 39

y = 19

The bigger number is 39 and the smaller number is 19.