# Question 7f121

Jan 30, 2017

The number is $60$.

#### Explanation:

Hey Sophie, you're not dumb at all. Let's break up this problem.

A percent is one-hundredth of any number. By inference, twenty percent (20%) is twenty-hundredths of any number, which is the same as saying the product of the number and $\frac{20}{100}$.

Now there are three factors here:
1. The number
2. The percentage
3. The percent amount (the product)

If we know any two of these, the third can be calculated easily. We can use the formula:

$n \times p = a$

where n=number, p=percent, and a=percent amount.

From the data you have given, we know p (20%# or $\frac{20}{100}$) and a ($12$), hence:

$n \times \frac{20}{100} = 12$

Reduce the fraction $\frac{20}{100}$ by dividing both the numerator and denominator by $20$.

$n \times \frac{1 \cancel{20}}{5 \cancel{100}} = 12$

$n \times \frac{1}{5} = 12$

Multiply both sides by $5$.

$n \times \frac{1}{5} \times 5 = 12 \times 5$

$n \times \frac{1}{1 \cancel{5}} \times 1 \cancel{5} = 60$

$n = 60$

Hence the number is $60$.