How do you solve \frac { 19} { x } = \frac { 38} { 100}?

Sep 8, 2017

$x = 50$

Explanation:

$\frac{19}{x} = \frac{38}{100}$

multiply both sides with $x$ to eliminate $x$ at $\frac{19}{x}$
$\frac{19}{x} \cdot x = \frac{38}{100} \cdot x$
$19 = \frac{38 x}{100}$

multiply $100$ to both sides
$19 \cdot 100 = \frac{38 x}{100} \cdot 100$
$1900 = 38 x$

divide $38$ to both sides to isolate $x$
$\frac{1900}{38} = \frac{38 x}{38}$

$50 = x$

Sep 8, 2017

Cross-multiply.

Explanation:

Solving implies we determine the value of $x$ in this equation.

In order to solve this, an easy way is to "cross-multiply".

If we were to apply this to our equation...

$\frac{19}{x} = \frac{38}{100}$

$19 \left(100\right) = 38 x$

$1900 = 38 x$

$50 = x$

We can check our work by subbing in $x = 50$ into the original equation.

$\frac{19}{x} = \frac{38}{100}$

$\frac{19}{50} = \frac{38}{100}$

If we simplify the right side of the equal sign.

$\frac{19}{50} = \frac{19}{50}$

They equal each other! This proves that $x = 50$.

Hope this helps :)