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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Keywords: mixed fraction, improper fraction, additional mixed fraction
