Question

If the third of three consecutive integers is subtracted from 132, the result is the sum of the first and second. What are the integers?

Answer 1

Three consecutive integers are 43, 44, 45

Explanation:

Let three consecutive integers be x, (x + 1), (x + 2)

According to the question, if the third of three consecutive integers is subtracted from 132, the result is the sum of the first and second.

`\therefore`

`\implies \rm 132 - (x + 2) = x + (x + 1) \\ \\ \implies \rm 132 - x - 2 = x + x + 1 \\ \\ \implies \rm 130 - x = 2x + 1 \\ \\ \implies \rm 130 - 1 = 2x + x \\ \\ \implies \rm 129 = 3x \\ \\ \implies \rm 3x = 129 \\ \\ \implies \rm x = (129)/(3) \\ \\ \implies \rm x = 43`

So,

The integers are as follows:

x = 43

x + 1 = 44

x + 2 = 45

Answer 2

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Explanation: