Question

The sum of two numbers is 56, and their difference is 10. What are the numbers?

Answer 1

There are two equations hidden in the language here:

a + b = 56 and a - b = 10.

if you do (a+b) + (a-b) then you get:

(a+b) + (a-b) = 66 = a + b + a - b

The b's cancel, so you get 2a = 66, which means a = 33. You can use this to solve for b in one of the above equations by plugging in a = 33 and figuring out what b has to be. Then you will have your two numbers.

Answer 2

x + y = 56
x - y = 10 so x = y + 10
y + 10 + y = 56
2y +10 = 56
2y = 56 -10
2y = 46
y = 46/2
y = 23

x = y + 10 = 23 + 10 =33

Answer: The numbers are 23 and 33

Proof:

sum: 23 + 33 = 56
difference: 33 -23 = 10