Question

Marvin buys a hose that is 27 3/4 feet long He already owns a hose at home that is 2/3 the length of the new hose How many total yards of hose does Marvin have now?

Answer 1

Marvin has 15 5/12 yards.

Answer 2

The total yards of hose that Marvin has now is $15\frac{5}{12}$ yards

Further Explanation

New hose (x) : $27\frac{3}{4} feet$

at home hose (y) = $\frac{2}{3} x$

How many total yards of hose does Marvin have now?

First, we are going to calculate the long of the hose that Marvin already has:

$\boxed {y = \frac{2}{3} x }\\\boxed { = \frac{2}{3} \times \frac{111}{4} = \frac{222}{12} = 18 \frac{1}{2} }$

Total long of hose:

= new hose + at home hose

= x + y

$\boxed {= 27\frac{3}{4} + 18\frac{1}{2} }$

$\boxed {= 27+18 (\frac{3}{4} + \frac{1}{2}) }\\\boxed {= 45 (\frac{3+2}{4}) }\\\boxed {= 45\frac{5}{4} }\\ \boxed {= 46\frac{1}{4} }$

Total of the long hose Marvin has is $46\frac{1}{4}$ feet. The question asking the length in yards, so we need to convert feet to yards:

$1 foot = \frac{1}{3} yard$

$\boxed {= 46\frac{1}{4} feet \times\frac{1}{3} yard } \\\boxed {= \frac{185}{4} \times\frac{1}{3} }\\\boxed {= \frac{185}{12} = 15\frac{5}{12} }$

So the total yards of hose that Marvin has now is $15\frac{5}{12}$ yards

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