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 the hose does Marvin have now?

Correct answer:

x =  15 ⁵⁄₁₂ = 185/12 yd

Step-by-step explanation:

$$\begin{gathered} a=27\frac{3}{4}=27+\frac{3}{4}=\frac{27\cdot 4+3}{4}=\frac{108+3}{4}=\frac{111}{4}=27.75\text{ft} \\ b=\frac{2}{3}\cdot a=\frac{2}{3}\cdot \frac{111}{4}=\frac{2\cdot 111}{3\cdot 4}=\frac{222}{12}=\frac{37}{2}=18.5\text{ft} \\ c=a+b=\frac{111}{4}+\frac{37}{2}=\frac{111}{4}+\frac{74}{4}=\frac{111+74}{4}=\frac{185}{4}=46.25\text{ft} \\ x=c\to \text{yd}=c:3\text{yd}=46.25:3\text{yd}=15.417\text{yd}=\frac{185}{12}\text{yd}=15\frac{5}{12}\text{yd}=15.4167\text{yd} \end{gathered}$$

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