SOLUTION: Find all sets of 3 consecutive integers whose sum is between 95 and 115.

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Question 778125: Find all sets of 3 consecutive integers whose sum is between 95 and 115.
Answer by MathLover1(20850) About Me  (Show Source):
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let 3 consecutive integers be x,x%2B1,and x%2B2
if their sum is between 95 and 115, then we have
95%3Cx%2B%28x%2B1%29%2B%28x%2B2%29%3C115......solve for x
95%3Cx%2Bx%2B1%2Bx%2B2%3C115
95%3C3x+%2B3%3C115
95-3%3C3x+%2B3-3%3C115-3
92%3C3x%3C112
92%2F3%3C3x%2F3%3C112%2F3
30.67%3Cx%3C37.33
so, x could be any integer between 31 and 36
if x=31, then x%2B1=32,and x%2B2=33
or if x=34, then x%2B1=35,and x%2B2=36