# How do you solve 5/13=(k-4)/39?

Feb 25, 2017

$k = 19$

#### Explanation:

Multiply both sides of the equation by the $\textcolor{b l u e}{\text{lowest common multiple}}$ ( LCM) of 13 and 39

the LCM of 13 and 39 is 39

$\Rightarrow {\cancel{39}}^{3} \times \frac{5}{\cancel{13}} ^ 1 = {\cancel{39}}^{1} \times \frac{k - 4}{\cancel{39}} ^ 1$

$\Rightarrow 15 = k - 4 \leftarrow \textcolor{red}{\text{no fractions}}$

add 4 to both sides.

$15 + 4 = k \cancel{- 4} \cancel{+ 4}$

$\Rightarrow k = 19$

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

Substitute this value into the right side and if equal to the left side then it is the solution.

$\text{right side } = \frac{19 - 4}{39} = \frac{15}{39} = \frac{{\cancel{15}}^{5}}{\cancel{39}} ^ \left(13\right)$

$\Rightarrow k = 19 \text{ is the solution}$