Posted by **francis** on Thursday, October 12, 2006 at 3:22pm.

1. If the first and third of three consecutive odd integers are added, the result is 51 less than five times the second integer. Find the third integer.

Let the 3 numbers be x, (x + 1) and (x + 2).

Then, x + (x + 2) = 5(x + 1) - 51

Solve for x.

We want "three consecutive odd integers". These look like

2k+1, 2k+3, and 2k+5

We're told

2k+1 + 2k+5 = 5*(2k+3) - 51 so

4k+6 = 10k + 15 - 51 or after rearranging

42 = 6k and k=7 so the numbers are

15,17 and 19

Test:

15 + 19 = 5*17 -51 or

34 = 85 - 51

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