The sum of two numbers is 22. The sum of 4 times the larger and 5 times the smaller is 92. Find the numbers.

Answer 1

This is likely intended to be solved using one variable, but let's use two.

Let x = the smaller number

y = larger number

The sum of the two numbers is 22:

x + y = 22

So y = 22 - x (another way to represent the larger number in terms of the smaller.

4(22-x) is four times the larger

5x is 5 times the smaller.

4(22-x) + 5x = 92

88 - 4x + 5x = 92

x + 88 = 92

x = 4

y = 22 - 4 = 18

So the smaller is 4 and the larger is 18.

They do have a sum of 92.

4(18) + 5(4) = 72 + 20 = 92 (check)