# How do you use cross products to solve 3/x=4/28?

Jan 26, 2017

$x = 21$

#### Explanation:

$\frac{\textcolor{b l u e}{3}}{\textcolor{red}{x}} = \frac{\textcolor{red}{4}}{\textcolor{b l u e}{28}}$

Now multiply the $\textcolor{red}{\text{values in red}}$ together, the $\textcolor{b l u e}{\text{values in blue}}$ together and equate them.

As you can see, this multiplication forms a cross (X) hence the reason it is called cross products.

$\Rightarrow \textcolor{red}{4 x} = \left(\textcolor{b l u e}{3} \times \textcolor{b l u e}{28}\right)$

$\Rightarrow 4 x = 84$

To solve for x, divide both sides by 4

$\frac{\cancel{4} x}{\cancel{4}} = \frac{84}{4}$

$\Rightarrow x = 21$

$\textcolor{b l u e}{\text{As a check}}$

substitute this value into the equation and if the left side equals the right side for this value then it is the solution.

$\text{left side } = \frac{3}{21} = {\cancel{3}}^{1} / {\cancel{21}}^{7} = \frac{1}{7}$

$\text{right side } = \frac{4}{28} = {\cancel{4}}^{1} / {\cancel{28}}^{7} = \frac{1}{7}$

$\Rightarrow x = 21 \text{ is the solution}$

Jan 26, 2017

$x = 21$

#### Explanation:

$\frac{3}{x} = \frac{4}{28}$

$\frac{3}{x} = \frac{1}{7}$

Cross multiply:

$x \times 1 = 3 \times 7$

$x = 21$