Discussion
Three consecutive integers are such that when they are taken in increasing order and multiplied by 3, 5 and 2, respectively, they add up to 99. What is the sum of the original first and third integers ?
Answer: C
The sum of the first and third integers is 20.
Let the integers be n, n + 1 and n + 2:
\[ \begin{aligned} 3n + 5(n + 1) + 2(n + 2) &= 99 \\ 10n + 9 &= 99 \Rightarrow n = 9 \end{aligned} \]
The integers are 9, 10 and 11 (check: 27 + 50 + 22 = 99), so the first and third add up to 9 + 11 = 20. 18 and 24 are not sums of the first and third of three consecutive integers satisfying the condition.
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