Jared's room painting

Jared wants to paint his room. The dimensions of the room are 12 feet by 15 feet, and the walls are 9 feet high. There are two windows that measure 6 feet by 5 feet each. There are two doors, whose dimensions are 30 inches by 6 feet each. If a gallon of paint covers approximately 350 square feet, how many gallons of paint will it take to give two layers of paint to the walls?

Correct result:

x =  3.2914 gal

Solution:

$$\begin{gathered} a=12\text{ ft } \\ b=15\text{ ft } \\ c=9\text{ ft } \\ {w}_1=6\text{ ft } \\ {w}_2=5\text{ ft } \\ {d}_1=30\text{ inch}\to \text{ ft}=30\mathrm{/}12\text{ ft}=2.5\text{ ft } \\ {d}_2=6\text{ ft } \\ h=350{\text{ft}}^2\text{/gal } \\ {S}_1=a\cdot b+2\cdot (a+b)\cdot c=12\cdot 15+2\cdot (12+15)\cdot 9=666{\text{ft}}^2 \\ W=w_1\cdot w_2=6\cdot 5=30{\text{ft}}^2 \\ D=d_1\cdot d_2=2.5\cdot 6=15{\text{ft}}^2 \\ S=S_1-2\cdot W-2\cdot D=666-2\cdot 30-2\cdot 15=576{\text{ft}}^2 \\ x=2\cdot S\mathrm{/}h=2\cdot 576\mathrm{/}350={\displaystyle \frac{576}{175}}=3{\displaystyle \frac{51}{175}}=3.2914\text{ gal} \end{gathered}$$

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