Interior designer

To make draperies, an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20-yard bolts, how much will be left over after completing both draperies?

Correct answer:

x =  1/4 yd

Step-by-step explanation:

$$\begin{gathered} a=11\frac{1}{4}=11+\frac{1}{4}=\frac{11\cdot 4+1}{4}=\frac{44+1}{4}=\frac{45}{4}=11.25\text{yd} \\ b=8\frac{1}{2}=8+\frac{1}{2}=\frac{8\cdot 2+1}{2}=\frac{16+1}{2}=\frac{17}{2}=8.5\text{yd} \\ c=a+b=\frac{45}{4}+\frac{17}{2}=\frac{45}{4}+\frac{34}{4}=\frac{45+34}{4}=\frac{79}{4}=19.75\text{yd} \\ c<20\text{yd} \\ x=20-c=20-\frac{79}{4}=\frac{20\cdot 4}{4}-\frac{79}{4}=\frac{80}{4}-\frac{79}{4}=\frac{80-79}{4}=\frac{1}{4}=\frac{1}{4}\text{yd}=0.25\text{yd} \end{gathered}$$

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