Numbers

Algebra Level 2

The sum of two positive integers is 97.

If the larger number is divided by smaller number, the quotient is 7 and the remainder is 1.

Find the difference between the two numbers.

1 solution

Zee Ell
Feb 20, 2017

If our two numbers are a and b, a > b then:

$a = 7b + 1$

$a + b = 7b + 1 + 1= 97$

$8b + 1 = 97$

$b = 12$

$a = 7 × 12 + 1 = 85$

$a - b = \boxed {73}$