SOLUTION: Find three consecutive integers such that the sum of the first plus one-third of the second plus three-eighths of the third is 25.

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Question 563449: Find three consecutive integers such that the sum of the first plus one-third of the second plus three-eighths of the third is 25.
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let
First Number = x%2B1
Second Number=x%2B2
Third Number = x%2B3

Given
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sum of the first plus one-third of the second plus three-eighths of the third is 25.
%28x%2B1%29%2B%281%2F3%29%28x%2B2%29%2B%283%2F8%29%28x%2B3%29=25
%28x%2B1%29%2B%28x%2B2%29%2F3%2B%28%283%29%28x%2B3%29%29%2F8=25
%28x%2B1%29%2B%28x%2B2%29%2F3%2B%28%283%29%28x%2B3%29%29%2F8=25
%28x%2B1%29%2B%28x%2B2%29%2F3%2B%283x%2B9%29%2F8=25
Take LCD on R.H.S.
%2824%28x%2B1%29%2B8%28x%2B2%29%2B3%283x%2B9%29%29%2F24=25
%2824x%2B24%2B8x%2B16%2B9x%2B27%29%2F24=25
%2841x%2B67%29%2F24=25
Multiply by 24 both sides of above equation
%2824%29%2841x%2B67%29%2F24=%2825%29%2824%29
cross%2824%29%2841x%2B67%29%2Fcross%2824%29=600
41x%2B67=600
41x=600-67
41x=533
Divide by 41 both sides of above equation
41x%2F41=533%2F41
cross%2841%29x%2Fcross%2841%29=cross%28533%29%2Fcross%2841%29
x=13


First Number = x%2B1 = 13%2B1 = 14
Second Number=x%2B2 = 13%2B2 = 15
Third Number = x%2B3 = 13%2B3 = 16
Check
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sum of the first plus one-third of the second plus three-eighths of the third is 25.
14%2B%281%2F3%29%2815%29%2B%283%2F8%29%2816%29=25
14%2B15%2F3%2B48%2F8=25
14%2Bcross%2815%29%2Fcross%283%29%2Bcross%2848%29%2Fcross%288%29=25
14%2B5%2B6=25
25=25