Question

The larger of two numbers is eight more than four times the smaller number. The larger number is also thirty-eight more than three times the smaller number. What are the numbers?​

Answer 1

The numbers are 30 and 128

Explanation:

Let's call the smaller number S (for smaller) and the larger L (for larger).

"The larger of two numbers is eight more than four times the smaller number"

translates to

L = 4 * S + 8

"The larger number is also thirty-eight more than three times the smaller number"

translates to

L = 3 * S + 38

So we have 2 equations with 2 unknown variables - we can solve this.

4 * S + 8 = 3 * S + 38 // subtract 3*S from both sides

S + 8 = 38

S = 30

We have the smaller number, now for the larger

L = 4 * S + 8 = 4 * 30 + 8 = 128

or

L = 3 * S + 38 = 3 * 30 + 38 = 128