The total yards of hose that Marvin has now is [tex]15\frac{5}{12}[/tex] yards
New hose (x) : [tex]27\frac{3}{4} feet[/tex]
at home hose (y) = [tex]\frac{2}{3} x[/tex]
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:
[tex]\boxed {y = \frac{2}{3} x }\\\boxed { = \frac{2}{3} \times \frac{111}{4} = \frac{222}{12} = 18 \frac{1}{2} }[/tex]
Total long of hose:
= new hose + at home hose
= x + y
[tex]\boxed {= 27\frac{3}{4} + 18\frac{1}{2} }[/tex]
[tex]\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} }[/tex]
Total of the long hose Marvin has is [tex]46\frac{1}{4}[/tex] feet. The question asking the length in yards, so we need to convert feet to yards:
[tex]1 foot = \frac{1}{3} yard[/tex]
[tex]\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} }[/tex]
So the total yards of hose that Marvin has now is [tex]15\frac{5}{12}[/tex] yards
Fraction subtraction brainly.com/question/2727531
Mixed fraction (part to whole relationship) brainly.com/question/2954545
Mixed fraction brainly.com/question/745462
Keywords: mixed fraction, improper fraction, additional mixed fraction