Question

In a set of five consecutive integers, the smallest integer is more than $\frac23$ the largest. What is the smallest possible value of the sum of the five integers?

Answer 1

55

Explanation:

Answer 2

55

Explanation:

Let x represent the middle integer. Then the smallest is x-2 and the largest is x+2. Your requirement is that ...

(x-2)/(x+2) > 2/3

3x -6 > 2x +4 . . . . cross multiply

x > 10 . . . . . . . . . . .add 6-2x

The smallest integer satisfying this requirement is x=11. The sum of the 5 integers is 5x = 55.

The smallest sum is 55.