Hi, there--

THE PROBLEM:
The sum of two numbers, x and y is 86. Their difference is 38. Find the numbers.

A SOLUTION:
Let x be the greater number.
Let y be the lesser number.

The sum of the two numbers is 86. The sum of x and y is x + y. This is equal to 86. We have
x + y = 86

The difference between x and y is x - y. The difference equals 38, so
x - y = 38

Therefore the system of equations is 
x + y = 86
x - y = 38

Use the elimination method to solve for x. Add the first and second equation together.
x + y = 86
x - y = 38
-------------
2x = 124
x = 62

The first number is 62.

Substitute 62 for x in the first equation.
x + y = 86
(62) + y = 86
y = 86 - 62
y = 24

The numbers are 62 and 24.

Check your answer using the words of the problem.

"The sum of two numbers is 86." Yes, the sum of 62 and 24 is 86. Check!
"Their difference is 38." Yes, 62 minus 24 is 38. Check!


Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com