SOLUTION: Find three consecutive positive intergers such that the product of the first and second integers is 26 less than the product of the second and third. i have no idea how to set t

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Find three consecutive positive intergers such that the product of the first and second integers is 26 less than the product of the second and third. i have no idea how to set t      Log On


   



Question 600262: Find three consecutive positive intergers such that the product of the first and second integers is 26 less than the product of the second and third.
i have no idea how to set this up!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 3 consecutive positive integers =
+n+
+n+%2B+1+
+n+%2B+2+
given:
+n%2A%28+n+%2B+1+%29+=+%28+n+%2B+1+%29%2A%28+n+%2B+2+%29+-+26+
---------
+n%5E2+%2B+n+=+n%5E2+%2B+3n+%2B+2+-+26+
Subtract +n%5E2+ from both sides
+n+=+3n+%2B+2+-+26+
+n+=+3n+-+24+
+2n+=+24+
+n+=+12+
+n+%2B+1+=+13+
+n+%2B+2+=+14+
The 3 consecutive positive integers are 12, 13, and 14
check:
+n%2A%28+n+%2B+1+%29+=+%28+n+%2B+1+%29%2A%28+n+%2B+2+%29+-+26+
+12%2A13+=+13%2A14+-+26+
+156+=+182+-+26+
+156+=+156+
OK