Question

Three consecutive integers, when taken in increasing order and multiplied by 2, 3 and 4 respectively, total up to 74. Find the three numbers.

Answer 1

Let the 3 consecutive integers be ‘x’, ‘x + 1’ and ‘x + 2’

Given that when multiplied by 2, 3 and 4 respectively and added up, we get 74

i.e. 2 × x + 3 × (x + 1) + 4 × (x + 2) = 74

Simplifying the equation, we get

2x + 3x + 3 + 4x + 8 = 74

9x + 11 = 63

9x = 63 ⇒ x = `63/9` = 7

First number = 7

Second numbers = x + 1 ⇒ 7 + 1 = 8

Third numbers = x + 2 ⇒ 7 + 2 = 9

∴ The numbers are 7, 8 and 9