Question

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

Answer 1

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