Question

Find five consecutive integers such that:

“The sum of the first and 3 times the fourth is equal to 39 less than twice the sum of the second, third, and fifth.”

Make sure to list ALL five integers in your answer and show all of your work!!

Answer 1

17, 18, 19, 20, 21

Explanation:

Let x represent the third (middle) integer. Then the first is (x-2) and the given relation is ...

(x-2) + 3(x+1) = -39 +2((x-1)+x+(x+2))

4x +1 = 6x -37 . . . . simplify

38 = 2x . . . . . . . . . add 37-4x

x = 19 . . . . . . . . . . divide by 2

The integers are ...

17, 18, 19, 20, 21

______

Check

17 + 3·20 = -39 +2(18 +19 +21)

17 +60 = -39 +2(58)

77 = -39 +116 . . . . . yes