SOLUTION: Find three consecutive odd integers such that the sum of the two smaller numbers and twice the largest is 158. My new age is the same as the largest number.

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Question 1169942: Find three consecutive odd integers such that the sum of the two smaller numbers and twice the largest is 158. My new age is the same as the largest number.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Informally....

The problem basically says that the sum of 4 odd integers that are close together is 158. 158 divided by 4 is 39.5; so the three odd integers are almost certainly 37, 39, and 41.

CHECK: 37+39+41+41 = 158

ANSWER: The three numbers are 37, 39, and 41.

(2) Formally

Let the three integers be x-2, x, and x+2. Then

%28x-2%29%2B%28x%29%2B2%28x%2B2%29+=+158
4x%2B2+=+158
4x+=+156
x+=+39

The numbers are
x-2 = 37
x = 39
x+2 = 41

NOTE:

You could of course start the algebraic solution using x, x+2 and x+4 as the three consecutive odd integers. However, in many problems like this involving three consecutive odd (or even) integers, the algebra required to finish the solution is easier if you use x to represent the middle number rather than the smallest.