Question

One fourth of a number decreased by 10, is -50. How do you find the number?

Answer 1

The number is -160 as shown in the explanation.

Explanation:

First, let's take each part of the question and write it in mathematical terms.

"One fourth of a number:

Let's call "a number" `n`. Then we can write "One fourth of this as:

`1/4 xx n`

"decreased by ten" can now be added to the previous term to give:

`(1/4 xx n) - 10`

"is `-50`

"is" is the same as "=" and `-50` is, well, `-50`.

`(1/4 xx n) - 10 = -50`

We can now solve this for `n` while always keeping the equation balanced:

`(1/4 xx n) - 10 + 10 = -50 + 10`

`(1/4 xx n) - 0 = -40`

`1/4 xx n = -40`

`4 xx 1/4 xx n = 4 xx -40`

`4/4 xx n = -160`

`1 xx n = -160`

`n = -160`