SOLUTION: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91.      Log On


   

Question 159650: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the 4 consecutive integers n,n%2B1,n%2B2,n%2B3
given:
2%2A%28%28n%2B2%29%2B%28n%2B3%29%29+=+3n+%2B+91
This is 1 equation and 1 unknown, so I should be able to solve
2%2A%282n+%2B+5%29+=+3n+%2B+91
4n+%2B+10+=+3n+%2B+91
n+%2B+10+=+91
n+=+81
The 4 consecutive integers are 81,82,83, and 84
check:
2%2A%28%28n%2B2%29%2B%28n%2B3%29%29+=+3n+%2B+91
2%2A%28%2881%2B2%29%2B%2881%2B3%29%29+=+3%2A81+%2B+91
2%2A%2883+%2B+84%29+=+243+%2B+91
2%2A167+=+334
334+=+334
OK