Question

There are three consecutive integers that sum to - 51. What is the product of half the smaller and half the largest?

Answer 1

The three consecutive integers that sum to -51 are -18, -17, and -16. The product of half the smaller integer and half the largest integer is 72.

Step-by-step explanation:

To find the three consecutive integers that sum to -51, we can let the smallest integer be x. The next two consecutive integers would then be x + 1 and x + 2. The sum of these three integers can be expressed as:

x + (x + 1) + (x + 2) = -51

Simplifying this equation, we get:

3x + 3 = -51

Now, we can solve for x:

3x = -54

x = -18

So the three consecutive integers are -18, -17, and -16. Now, we can find the product of half the smaller integer (-18/2 = -9) and half the largest integer (-16/2 = -8), which is:

-9 * -8 = 72