George

George decided to use blue paint to paint a wall with two windows. The wall is 12 7/8 ft by 8 ft. Both windows are 3 1/2 ft by 4 1/2 ft rectangles.

Find the area the paint needs to cover.

Correct answer:

A =  71 ¹⁄₂ = 143/2 ft²

Step-by-step explanation:

$$\begin{gathered} w=12\frac{7}{8}=12+\frac{7}{8}=\frac{12\cdot 8+7}{8}=\frac{96+7}{8}=\frac{103}{8}=12.875\text{ft} \\ l=8\text{ft} \\ x=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3.5\text{ft} \\ y=4\frac{1}{2}=4+\frac{1}{2}=\frac{4\cdot 2+1}{2}=\frac{8+1}{2}=\frac{9}{2}=4.5\text{ft} \\ n=2 \\ {A}_1=w\cdot l=\frac{103}{8}\cdot 8=\frac{103\cdot 8}{8}=\frac{824}{8}=103{\text{ft}}^2 \\ {A}_2=x\cdot y=\frac{7}{2}\cdot \frac{9}{2}=\frac{7\cdot 9}{2\cdot 2}=\frac{63}{4}=15.75{\text{ft}}^2 \\ A=A_1-2\cdot A_2=103-2\cdot \frac{63}{4}=\frac{143}{2}{\text{ft}}^2=71\frac{1}{2}{\text{ft}}^2=71.5{\text{ft}}^2 \end{gathered}$$

Try another example