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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.
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Solution
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
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