# Question #c1e7f

May 11, 2016

k = $\frac{21}{8}$ or $2.625$

#### Explanation:

We have
$\frac{2}{3} + 8 \frac{k}{4} = \frac{71}{12}$

Subtract 2/3 from both sides
$\left(\frac{2}{3} - \frac{2}{3}\right) + 8 \frac{k}{4} = \frac{71}{12} - \frac{2}{3}$

Write 2/3 as 8/12 (multiply 4 in both numerator and denominator)

$8 \frac{k}{4} = \frac{71}{12} - \frac{8}{12}$

Take $\frac{1}{12}$ common

$8 \frac{k}{4} = \left(71 - 8\right) \times \frac{1}{12}$

Divide by 2 on both sides
$8 \frac{k}{4 \times 2} = \frac{1}{2} \times \frac{63}{12}$

You have
$\cancel{8} \frac{k}{\cancel{8}} = \frac{63}{24}$

k = 63/24

Divide by both numerator and denominator by 3

$k = \frac{\frac{63}{3}}{\frac{24}{3}}$

$k = \frac{21}{8}$ or $2.625$