A costume designer has 40 yards of red fabric to make costumes for a musical in which 8 performers will wear red dresses and 14 people will wear red scarves. The costume maker user 3 1/2 yds for each dress and 3/4 yard for a scarf. After making the dresses and scarves, the costume designer uses the leftover fabric to make some sashes for the dresses. If each sash uses 1/4 yard of fabric, how many sashes can be made?

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chisnau chisnau · Answer 1 · 2018-11-15T08:53:29+01:00

Total fabric available = 40 yards

Number of dresses to be made = 8

Number of scarves to be made = 14

Amount of fabric used to make one dress = [tex]3\frac{1}{2}=\frac{7}{2}[/tex]

So fabric used to make 8 dresses = [tex]8\times\frac{7}{2}=28[/tex] yards

Amount of fabric used to make 1 scarf = [tex]\frac{3}{4}[/tex]

Fabric used to make 14 scarves = [tex]14\times\frac{3}{4}=10.5[/tex] or [tex]10\frac{1}{2}=\frac{21}{2}[/tex] yards

Hence, total fabric used to make dresses and scarves = [tex]28+\frac{21}{2}=\frac{56+21}{2}=\frac{77}{2}[/tex]

Leftover fabric = [tex]40-\frac{77}{2}=\frac{80-77}{2}=\frac{3}{2}[/tex] yards

[tex]\frac{1}{4}[/tex] yards is used to make = 1 sash

1 yard is used to make = [tex]\frac{1}{\frac{1}{4}}[/tex] sach

[tex]\frac{3}{2}[/tex] yards is used to make = [tex]4\times\frac{3}{2}=6[/tex]

Hence, 6 sashes can be made.