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Question
The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.
Options
112
126
119
116
Solution
112
Explanation:
Let the three consecutive multiples of 7 be 7x, (7x + 7), (7x + 14) where x is a natural number.
According to the question,
7x + (7x + 7) + (7x + 14) = 357
⇒ 21x + 21 = 357
⇒ 21(x + 1) = 357
⇒ `(21(x + 1))/21 = 357/21` ...[Dividing both sides by 21]
⇒ x + 1 = 17
⇒ x = 17 – 1 ...[Transposing 1 to RHS]
⇒ x = 16
Hence, the smallest multiple of 7 is 7 × 16, i.e. 112.
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