Question

question 24 (4 points)
you want to determine how many gallons of paint you need to buy to paint your bedroom. when youre painting a room, you need to determine how many square feet you intend to cover. when measuring a wall, dont include baseboards, crown molding, or other trim, as youre likely to be painting those with a different type of paint or color. to get an accurate measurement, you will want to first find the area of your walls and then subtract the area of any doors and/or windows that you have in your room. remember the area of a rectangle equals length times width.
there are 4 walls in your room that you want to paint. each wall is 14 feet by 16 feet. find the total area of all 4 walls. hint: for this question, pretend there are no doors or windows in this room. the total area of all 4 walls is ________ square feet.
next, you will need to subtract the area of any windows and/or doors in your room. you have 2 windows and 1 door in your room. the area of each window is 15 square feet and the area of each door is 20 square feet. the total area that will need to be painted is ________ square feet.
each gallon of paint covers 400 square feet. how many gallons of paint will you need to buy? i will need to buy ____ gallons of paint. (round your answer to one decimal place.)
if your paint store only sells paint in gallons, how many gallons of paint do you need for this room? i will need to buy ______ gallons of paint. (round up to the nearest whole number.)

Explanation:

Step1: Calculate area of one wall

Each wall is a rectangle with length $l = 16$ feet and width $w=14$ feet. Using the formula for the area of a rectangle $A = l\times w$, the area of one wall is $A_1=16\times14 = 224$ square - feet.

Step2: Calculate total area of 4 walls

Since there are 4 walls, the total area of the 4 walls $A_{total - walls}=4\times A_1=4\times224 = 896$ square - feet.

Step3: Calculate total area of windows and door

There are 2 windows with each window having an area of 15 square feet and 1 door with an area of 20 square feet. The total area of windows and door $A_{windows - door}=2\times15 + 20=30 + 20=50$ square - feet.

Step4: Calculate area to be painted

The area to be painted $A_{paint}=A_{total - walls}-A_{windows - door}=896 - 50=846$ square - feet.

Step5: Calculate number of gallons (decimal)

Each gallon of paint covers 400 square feet. The number of gallons $n_1=\frac{A_{paint}}{400}=\frac{846}{400}=2.115\approx2.1$ gallons.

Step6: Calculate number of gallons (rounded up)

Rounding up 2.115 to the nearest whole number, we get $n_2 = 3$ gallons.

Answer:

896
846
2.1
3