Living room 3

Pearl wants to buy a carpet to cover her whole living room, except for the tiled floor. The tiled floor is 7 1/2 ft by 3 1/4 ft. The room has dimensions of 12 1/4 ft x 5 ft. Find the area the carpet needs to cover.

Correct answer:

A =  36 ⁷⁄₈ = 295/8 ft²

Step-by-step explanation:

$$\begin{gathered} a=7\frac{1}{2}=7+\frac{1}{2}=\frac{7\cdot 2+1}{2}=\frac{14+1}{2}=\frac{15}{2}=7.5\text{ft} \\ b=3\frac{1}{4}=3+\frac{1}{4}=\frac{3\cdot 4+1}{4}=\frac{12+1}{4}=\frac{13}{4}=3.25\text{ft} \\ x=12\frac{1}{4}=12+\frac{1}{4}=\frac{12\cdot 4+1}{4}=\frac{48+1}{4}=\frac{49}{4}=12.25\text{ft} \\ y=5\text{ft} \\ {S}_1=a\cdot b=\frac{15}{2}\cdot \frac{13}{4}=\frac{15\cdot 13}{2\cdot 4}=\frac{195}{8}=24.375{\text{ft}}^2 \\ {S}_2=x\cdot y=\frac{49}{4}\cdot 5=\frac{49\cdot 5}{4}=\frac{245}{4}=61.25{\text{ft}}^2 \\ A=S_2-S_1=\frac{245}{4}-\frac{195}{8}=\frac{490}{8}-\frac{195}{8}=\frac{490-195}{8}=\frac{295}{8}=\frac{295}{8}{\text{ft}}^2=36\frac{7}{8}{\text{ft}}^2=36.875{\text{ft}}^2 \end{gathered}$$

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