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

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Answer 1 · 2016-12-13T14:09:17

The number is -160 as shown in the 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:

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

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

$1/4 xx n = -40$

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

$4/4 xx n = -160$

$1 xx n = -160$

$n = -160$