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

Question 340948: 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 CharlesG2(834) (Show Source): You can put this solution on YOUR website!
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

x = first integer
x + 1 = 2nd integer
x + 2 = 3rd integer

x + 1/3 * (x + 1) + 3/8 * (x + 2) = 25
x + 1/3 * x + 1/3 + 3/8 * x + 6/8 = 25
1/3 = 8/24 = 4/12, 6/8 = 18/24 = 9/12, 4/12 + 9/12 = 13/12
x + 1/3 * x + 3/8 * x + 13/12 = 25
1 + 1/3 + 3/8 = 1 + 8/24 + 9/24 = 1 + 17/24 = 24/24 + 17/24 = 41/24
41/24 * x + 13/12 = 25
41x + 26 = 25 * 24 = 600
41x = 574
x = 574/41 = 14

the integers are 14, 15, and 16

check
x + 1/3 * (x + 1) + 3/8 * (x + 2) = 25
14 + 1/3 * 15 + 3/8 * 16 = 25
14 + 5 + 6 = 25
25 = 25

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