Question

One number exceeds another number by 6. One fourth of the sum of the two numbers is two less than the smaller.

Find the numbers.

Answer 1

7 and 13

Explanation:

let the 2 numbers be x and y , x > y , then

x = y + 6 → (1)

`(1)/(4)` (x + y) = y - 2 ( multiply both sides by 4 to clear the fraction )

x + y = 4y - 8 ( subtract 4y from both sides )

x - 3y = - 8 → (2)

Substitute x = y + 6 into (2)

y + 6 - 3y = - 8

- 2y + 6 = - 8 ( subtract 6 from both sides )

- 2y = - 14 ( divide both sides by - 2 )

y = 7

Substitute y = 7 into (1)

x = 7 + 6 = 13

The 2 numbers are 7 and 13