Consecutive integers

Question

The sum of three consecutive odd integers is -57. Find the three odd integers

Answer 1

Hi Angela.

To solve this problem, you have to keep in mind that odd numbers are separated by even numbers. For example, 1 is an odd number, then 3 is an odd number, and then 5 is an odd number, and so on. So if we wanted to know the difference between 3 and 1 or 5 and 3, it would be 2 (you'd subtract 1 from 3 or 3 from 5). Similarly, the difference between the first odd number in this sequence of three odd numbers (1) and the last (5) is 4 because 5-1 = 4.

Keep in mind, too, that we don't know what the odd numbers are. What we are going to do is use "x" to stand for the first odd number and then add 2 to it for the next odd number and 4 So, when we add up three consecutive odd numbers, we need to write it like this:

x + (x + 2) + (x + 4) = -57. Combine like terms on the left side of the equal sign

3x + 6 = -57 Subtract six from the left side and the right side of the equation

3x = -63 Divide each side by 3 to get "x" alone

x = -21

So the first number in our sequence of three odd numbers is -21. If we add two to that number, we'll get the second number in our sequence and if we add four to it we'll get the third number in our sequence.

-21 + 2 = -19

-21 + 4 = -17

So the three numbers are -21, -19, and -17.

To be sure we are right, let's add them up and see if they equal -57.

-21 + -19 + -17 = -21-19-17 = -57 We got it right!!

Answer 2

X+X+2+X+4=57

3X+6=57

3X+6-6 =57-6

3X=51

X-17

X=2=19

X=4=21

so: 17+19+21=57

Answer 3

The difference between an odd number and the next odd number is two. For example, 5-3 = 2 and 3-1 = 2.

So three odd numbers can be represented as x, x+2, and x+4.

Here, the three odd numbers add up to -57.

Thus:

x + (x + 2) + (x + 4) = -57

3x + 6 = -57

3x = -63

x = -21

So the first odd number is -21. The second odd number must be -19 and the third odd number must be -17.

Let's check to see if we got it right:

-21 + -19 + -17 = -21 - 19 - 17 = -57.

We got it right!