# Given that 5(19/15)+5y=9 what is the value of y?

Feb 20, 2017

$y = \frac{8}{15}$

#### Explanation:

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

$5 \left(\frac{19}{15}\right)$ is the same as $5 \times \frac{19}{15}$

It is also the same as: $\frac{5}{15} \times 19 \text{ "->" } \frac{{\cancel{5}}^{1}}{{\cancel{15}}^{3}} \times 19$

Write as: $\frac{19}{3} + 5 y = 9$

subtract $\frac{19}{3}$ from both sides

$5 y = 9 - \frac{19}{3}$

but 9 is the same as $\frac{27}{3}$

$5 y = \frac{27 - 19}{3} = \frac{8}{3}$

Divide both sides by 5

$y = \frac{8}{3 \times 5} = \frac{8}{15}$
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$\textcolor{b l u e}{\text{Approach 2}}$

$5 \left(\frac{19}{15}\right) + 5 y = 9$

Factor out the 5

$5 \left(\frac{19}{15} + y\right) = 9$

divide both sides by 5

$\frac{19}{15} + y = \frac{9}{5}$

Subtract $\frac{19}{15}$ from both sides

$y = \frac{9}{5} - \frac{19}{15}$

$y = \frac{27}{15} - \frac{19}{15} = \frac{8}{15}$