# 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?

Result

x =  3.291 gal

#### Solution:

$a=12 \ \text{ft} \ \\ b=15 \ \text{ft} \ \\ c=9 \ \text{ft} \ \\ \ \\ w_{1}=6 \ \text{ft} \ \\ w_{2}=5 \ \text{ft} \ \\ \ \\ d_{1}=30 \ inch=30 / 12 \ ft=2.5 \ ft \ \\ d_{2}=6 \ \text{ft} \ \\ \ \\ h=350 \ \text{ft}^2\text{/gal} \ \\ \ \\ S_{1}=a \cdot \ b + 2 \cdot \ (a+b) \cdot \ c=12 \cdot \ 15 + 2 \cdot \ (12+15) \cdot \ 9=666 \ \text{ft}^2 \ \\ W=w_{1} \cdot \ w_{2}=6 \cdot \ 5=30 \ \text{ft}^2 \ \\ D=d_{1} \cdot \ d_{2}=2.5 \cdot \ 6=15 \ \text{ft}^2 \ \\ \ \\ S=S_{1} - 2 \cdot \ W-2 \cdot \ D=666 - 2 \cdot \ 30-2 \cdot \ 15=576 \ \text{ft}^2 \ \\ \ \\ x=2 \cdot \ S/h=2 \cdot \ 576/350 \doteq \dfrac{ 576 }{ 175 } \doteq 3.2914 \doteq 3.291 \ \text{gal}$

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