Sportwear

A sporting goods manufacturer has 11 2/9 yd of fabric to make soccer shorts. Each pair of soccer shorts requires 3/8 yd of fabric. How many pairs of soccer shorts can be​ made? How much material will be left​ over?

Correct answer:

n =  29
x =  25/72 yd

Step-by-step explanation:

$$\begin{gathered} a=11\frac{2}{9}=11+\frac{2}{9}=\frac{11\cdot 9+2}{9}=\frac{99+2}{9}=\frac{101}{9}=11\frac{2}{9}\doteq 11.2222\text{yd} \\ b=3/8=\frac{3}{8}=0.375\text{yd} \\ {n}_1=a/b=\frac{101}{9}/\frac{3}{8}=\frac{101}{9}:\frac{3}{8}=\frac{101}{9}\cdot \frac{8}{3}=\frac{101\cdot 8}{9\cdot 3}=\frac{808}{27}\doteq 29.9259 \\ n=\lfloor n_1\rfloor =\lfloor 29.9259\rfloor =29 \end{gathered}$$

$$\begin{gathered} c=n\cdot b=29\cdot \frac{3}{8}=\frac{29\cdot 3}{8}=\frac{87}{8}=10.875\text{yd} \\ x=a-c=\frac{101}{9}-\frac{87}{8}=\frac{808}{72}-\frac{783}{72}=\frac{808-783}{72}=\frac{25}{72}=\frac{25}{72}\text{yd}=0.3472\text{yd} \end{gathered}$$

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