The sum of three consecutive integers is −384

Question

The sum of three consecutive integers is . Find the three integers.

Answer 1

"three consecutive integers" may be:

x (x+1) (x+2)

or

(y-1) y (y+1)

or

z (z+1) (z+2)

Now, you may solve this problem by adding the three numbers, setting the sum equal to (-384), and solving for the variable. Be careful to report the variable(s) that the question asks you to find.

Let's select the second strategy and solve for y:

(y-1) + y + (y+1) = -384

3y = - 384

y = -128 [Later you will learn that (sum of values) / (count of values) = average (in middle) ]

The numbers are -129, -128, and -127.

Now, note that -384/3 is -128 (that is, the average)

Answer 2

The 3 consecutive integers must all be negative to have a negative sum.

-x - (x-1) - (x-2) = -384

-x -x + 2 - x + 2 = -384. Recall that -(-a) = +a.

-3x + 3 = -384

-3x = -384 - 3 = -387

x = -129. x-1 = -128. x-2 = -127. -(129+128+127) = - 384.