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 sets of draperies?

Correct result:

x =  0.25 yd

Solution:

$$\begin{gathered} a=11+1\mathrm{/}4={\displaystyle \frac{45}{4}}=11.25\text{ yd } \\ b=8+1\mathrm{/}2={\displaystyle \frac{17}{2}}=8.5\text{ yd } \\ c=a+b=11.25+8.5={\displaystyle \frac{79}{4}}=19.75\text{ yd } \\ c<20 \\ x=20-c=20-19.75={\displaystyle \frac{1}{4}}={\displaystyle \frac{1}{4}}\text{ yd}=0.25\text{ yd} \end{gathered}$$

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