SOLUTION: The numbers on three raffle tickets are consecutive integers whose sum is 7530. Find the integers.

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Question 963526: The numbers on three raffle tickets are consecutive integers whose sum is 7530. Find the integers.
Answer by hkwu(60) About Me  (Show Source):
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Let a, b, c denote your integers. WLOG, assume that c is the largest integer. Then
c=b%2B1
b=a%2B1
and
a%2Bb%2Bc=7530
Substituting, we get
a%2B%28a%2B1%29%2B%28b%2B1%29=7530
a%2Ba%2B1%2B%28%28a%2B1%29%2B1%29=7530
3a%2B3=7530
3a=7527
a=2509
Thus a = 2509, b = 2510, and c = 2511.
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