Question

The larger of two numbers is 11 more than twice the smaller number. The sum of the numbers is 1 less than seven times the smaller numbers. Find the numbers.

Answer 1

The numbers are 3 and 17.

Explanation:

Let a and b respectively represent the larger and smaller numbers. We have:

`a =2b + 11`

`a + b = 7b- 1`

Substitute the top equation into the bottom equation, solve for b, and then find a.

`2b + 11 + b = 7b - 1`

`3b + 11 = 7b - 1`

`4b = 12`

`b = 3`

`a = 2(3) + 11 = 6 + 11 = 17`