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.

Question

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

Answer 1

X+x+2=5x+5-15
2x+2=5x-10
2+10=5x-2x
12=3x
3x/3=12/3
X=4.