# Question #be455

Jan 9, 2018

$p = \frac{3}{5}$

#### Explanation:

$\text{here are two possible approaches }$

$\textcolor{b l u e}{\text{Approach 1}}$

$\text{add the fractions on the left }$

$\text{the "color(blue)"lowest common multiple of 3 and 2 is 6}$

$\Rightarrow \frac{5}{3} \times \frac{2}{2} p = \frac{10}{6} p \text{ and } \frac{3}{2} \times \frac{3}{3} p = \frac{9}{6} p$

$\Rightarrow \frac{10}{6} p + \frac{9}{6} p = \frac{19}{10}$

$\Rightarrow \frac{19 p}{6} = \frac{19}{10}$

$\text{multiply all terms by 30}$

${\cancel{30}}^{5} \times \frac{19 p}{\cancel{6}} ^ 1 = {\cancel{30}}^{3} \times \frac{19}{\cancel{10}} ^ 1$

$\Rightarrow 95 p = 57$

$\text{divide both sides by 95}$

$\Rightarrow p = \frac{57}{95} = \frac{3}{5}$

$\textcolor{b l u e}{\text{Approach 2}}$

$\text{multiply all terms by the lowest common multiple}$

$\text{the lowest common multiple of 3, 2 and 10 is 30}$

$\Rightarrow 50 p + 45 p = 57$

$\Rightarrow 95 p = 57$

$\Rightarrow p = \frac{57}{95} = \frac{3}{5}$