Question

The product of two consecutive positive integers is 20 more than seven times the larger integer find the integers

Answer 1

9, 10

Explanation:

let x be the larger integer and y the smaller

x × y = 7x + 20

y + 1 = x [consecutive]

substitute

(y + 1)y = 7(y + 1) + 20

y² + y = 7y + 7 + 20

y² + y - 7y - 7 - 20 = 0

y² - 6y - 27 = 0

(y - 9) (y + 3) = 0

y = 9

y = -3 [discarded as it must be a POSITIVE INTEGER]

y + 1 = x

9 + 1 = x

x = 10