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

Dec 13, 2016

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:

$\frac{1}{4} \times n$

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

$\left(\frac{1}{4} \times n\right) - 10$

"is $- 50$

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

$\left(\frac{1}{4} \times n\right) - 10 = - 50$

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

$\left(\frac{1}{4} \times n\right) - 10 + 10 = - 50 + 10$

$\left(\frac{1}{4} \times n\right) - 0 = - 40$

$\frac{1}{4} \times n = - 40$

$4 \times \frac{1}{4} \times n = 4 \times - 40$

$\frac{4}{4} \times n = - 160$

$1 \times n = - 160$

$n = - 160$