Marvin

Marvin buys a hose that is 27 ¾ feet long. He already owns a hose at home that is ⅔ the length of the new hose. How many total yards of hose does Marvin have now?

Correct result:

x =  15.4167 yd

Solution:

$$\begin{gathered} a=27{\displaystyle \frac{3}{4}}={\displaystyle \frac{27\cdot 4+3}{4}}={\displaystyle \frac{111}{4}}=27.75\text{ ft } \\ b={\displaystyle \frac{2}{3}}\cdot a={\displaystyle \frac{2}{3}}\cdot 27.75={\displaystyle \frac{37}{2}}=18{\displaystyle \frac{1}{2}}=18.5\text{ ft } \\ c=a+b=27.75+18.5={\displaystyle \frac{185}{4}}=46{\displaystyle \frac{1}{4}}=46.25\text{ ft } \\ x=c\to \text{ yd}=c\mathrm{/}3\text{ yd}=46.25\mathrm{/}3\text{ yd}=15.417\text{ yd}=15.4167\text{ yd} \end{gathered}$$

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