Question

How do you find 3 consecutive odd integers where the sum is -141?

Answer 1

See a solution process below:

Explanation:

Let's call the first odd integer: `n`

Then the next two consecutive odd integers will be:

`n + 2` and `n + 4`

We can then write this equation and solve for `n`;

`n + (n + 2) + (n + 4) = -141`

`n + n + 2 + n + 4 = -141`

`n + n + n + 2 + 4 = -141`

`1n + 1n + 1n + 2 + 4 = -141`

`(1 + 1 + 1)n + (2 + 4) = -141`

`3n + 6 = -141`

`3n + 6 - color(red)(6) = -141 - color(red)(6)`

`3n + 0 = -147`

`3n = -147`

`(3n)/color(red)(3) = -147/color(red)(3)`

`(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = -49`

`n = -49`

Therefore:

`n + 2 = -49 + 2 = -47`

`n + 4 = -49 + 4 = -45`

The 3 consecutive odd integers summing to -141 are: -49, -47, -45

Solution Check:

`-49 - 47 - 45 = -96 - 45 = -141`

Answer 2

the three numbers are -49,-47 and -45

Explanation:

Let the first odd number be `x`
Then, the consecutive odd number is `x+2`
The last consecutive odd number is `x+4`

Why do we add 2 to each odd number?
Well, think of any three consecutive odd numbers.

135,137,139
186395,186397,186399

From the above, you can see that when you minus 2 consecutive numbers, you will always get a difference of 2

Since their sum equals to `-141`,

`x+(x+2)+(x+4)=-141`
`3x+6=-141`
`3x=-147`
`x=-49`

Therefore, your first odd number is -49
Your second number is `-49+2=-47`
Your third number is `-47+2=-45`

Now, just to make sure you are right, add the numbers together

`-49-47-45=-141`