Question

The sum of two consecutive ODD integers is -76. Find the integers.​

Answer 1

First number: -39

Second number: -37

Explanation:

An odd number can be written as
`2n+1` where n is a whole number.

Let's call our first number 2n+1.

Our second, consecutive number will be 2 more than our first number, since it has to be odd. All numbers go: odd -> even -> odd -> even. If we have an odd number, and add 2, we'll get the next odd number.

First number: 2n+1

Second number: 2n+1+2 = 2n+3

The sum of these two numbers, 2n+1 and 2n+3 will be -76.

(2n+1) + (2n+3) = -76

2n + 2n + 1 + 3 = -76

4n + 4 = -76

4n = -80

n = -20

Since our first number is 2n+1:

2 * (-20) + 1 = -40 + 1 = -39

First number: -39

Our second number is 2n+3, or 2 more than our first number.

-39 + 2 = -37

Second number: -37

We can double check this:

-39 + (-37) = -39 - 37 = -76