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Question
The sum of three consecutive integers is 5 more than the smallest of the integers. Find the integers.
Solution
Let one number be x
Then, the next two consecutive numbers will be x + 1 and x + 2
Sum of these three numbers = x + (x + 1) + (x + 2) = 3x + 3
According to the question,
3x + 3 = x + 5
⇒ 3x – x = 5 – 3 ......[Transposing x to LHS and 3 to RHS]
⇒ 2x = 2
⇒ `(2x)/2 = 2/2` .......[Dividing both sides by 2]
⇒ x = 1
∴ Hence, the numbers are 1, 1 + 1, 1 + 2 i.e., 1, 2, 3.
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