The sum of two numbers is 38 and the difference is 8 . What are the numbers?

Question

Please help me, much appreciated.

Answer 1

This type of problem is easy if you just think of the numbers as variables.  Then you can interpret the statements in the problem as equations.

 

So let x equal one of the numbers and let y be the other.  And let's assume that x is the larger of the two.

 

So that results in two equations:

 

x + y = 38

x - y = 8

 

These equations are easy to solve together.  First just add them together:

2x = 46

 

Divide both sides by 2

x = 23

 

Since the sum is 38, y must be 15.

 

And indeed the difference between 23 and 15 is 8, so it's correct.