# 10.5% of what number is 420?

Number is 4000.

#### Explanation:

Let the number be $x$.

$\therefore$ $x \left(\frac{105}{1000}\right) = 420$
$\Rightarrow$ $x = \frac{\cancel{420} \cdot 1000}{\cancel{105}} = \left(4 \cdot 1000\right) = 4000$

May 9, 2017

10.5% of 4000 is $420$

#### Explanation:

We know that 10.5% of the number we will call $N$ is $420$.
We know that $100$ of the number is $N$.

So now we can equate the two lines above by following what we have written:

$\frac{10.5}{100} = \frac{420}{N}$

Then cross multiply:

$10.5 N = 100 \cdot 420$

$\cancel{10.5} N = 100 \cdot \cancel{420} 4$

$N = 4000$

To check this answer we can calculate 10% or 1/10 of 4000 = 400

which is reasonably close to the 10.5% being $420$ as given above.