# Question #75b7f

Nov 30, 2016

60 books were donated.

#### Explanation:

What we are looking for is:

48 is 80% of what?

In mathematics "is" means "$=$".

"Percent" or "%" means "out of 100" or "per 100", Therefore 80% can be written as $\frac{80}{100}$.

When dealing with percents the word "of" means "times" or "to multiply".

And we can call "what" $n$.

So putting this altogether gives:

$48 = \frac{80}{100} \cdot \times n$

Solving for $n$ gives:

$\frac{100}{80} \times 48 = \frac{100}{80} \times \frac{80}{100} \times n$

$\frac{4800}{80} = \frac{8000}{8000} x n$

$60 = n$

Nov 30, 2016

The count of donated books was 60

#### Explanation:

The symbol % is a unite of measurement worth $\frac{1}{100}$

So 80% $\to \frac{80}{100}$

Let the total count of books donated be $x$
Given that the count sold is 48
Given that the percentage sold is 80%

$\frac{80}{100} \times x = 48$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If you multiply $\frac{80}{100} \text{ by } \frac{100}{80}$ you turn it into 1

So this is:

$\frac{80}{100} \times \frac{100}{80} = \frac{80 \times 100}{100 \times 80} = \frac{100 \times 80}{100 \times 80} = \frac{100}{100} \times \frac{80}{80} = 1 \times 1$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply both sides by $\frac{100}{80}$

$1 \times x = \frac{4800}{80} = 60$

$x = 60$