Paint and floor products often have estimates of how much product is needed. If we use these estimates along with the square area, we can estimate the cost of painting a room or finishing the floor of a room!
1.
A rectangular room is 14 feet long and 18 feet wide. The ceiling
is 8 feet from the floor. There are three windows, each of which are two
feet by three feet, and a doorway that is seven feet by three feet.
A can of paint estimates it will cover 400 square feet. It is recommended that two coats be used (the room will be painted twice). The paint costs $50 per can. How much will it cost to paint the room?
We can first calculate how many square feet the room would be if there were no windows and no doors, then subtract the square footage of the windows and doors.
There are two walls that are 14 feet long and 8 feet high. There are two walls that are 18 feet long and 8 feet high. The square footage of the walls is
\(2(14 \text{ feet} \cdot 8 \text{ feet}) + 2(18 \text{ feet} \cdot 8 \text{ feet}) =\)
\(2(112 \text{ feet}^2) + 2(144 \text{ feet}^2 ) =\)
\(224 \text{ feet}^2 + 288 \text{ feet}^2 =\)
\(512 \text{ feet}^2\)
Now, we calculate the square footage of the windows and the door. One window is
\(2\text{ feet} \cdot 3\text{ feet} =\)
\(6\text{ feet}^2\)
The door is
\(7 \text{ feet} \cdot 3 \text{ feet} =\)
\(21 \text{ feet}^2\)
Subtract three of the windows and one of the doors from the total square feet.
\(512 \text{ feet}^2 - 3 \cdot 6\text{ feet}^2 - 21 \text{ feet}^2 =\)
\(512 \text{ feet}^2 - 18\text{ feet}^2 - 21 \text{ feet}^2 =\)
\(473 \text{ feet}^2\)
We need to paint it twice for two coats, so the total amount to be painted is \(2 \cdot 473 \text{ feet}^2 = 946 \text{ feet}^2\). We cannot buy a fraction of a can of paint, so we must purchase 3 cans, as \(3 \cdot 400 \text{ feet}^2 = 1200 \text{ feet}^2\). The cost will be \(3 \cdot \$50 = \$150\).
2.
An oil based wood sealer costs $60 per gallon. One gallon covers
500 square feet. A rectangular room is 14 feet long and 18 feet wide. A
second rectangular room is 8 feet long by 10 feet wide. A person wants
three coats for both rooms with the sealer. How much will the project
cost?
First, we calculate the square footage to be covered.
\(\text{first room} + \text{second room} =\)
\(14 \text{ feet} \cdot 18 \text{ feet} + 8 \text{ feet} \cdot 10 \text{ feet} =\)
\(252 \text{ feet}^2 + 80 \text{ feet}^2 =\)
\(332 \text{ feet}^2\)
We want three coats, so we multiply the square footage by 3.
\(3 \cdot 332 \text{ feet}^2 = 996 \text{ feet}^2\)
As one can covers \(500\) square feet, we need to buy two cans, as it will cover \(1,000 \text{ feet}^2\). 2 cans will cost \(\$60 \cdot 2 = \$120\)
1. A rectangular room is 14 feet long and 18 feet wide. A second rectangular room is 8 feet long by 10 feet wide. The rooms are 8 feet tall. There are five windows in the two rooms, each of which are two feet by three feet. There are three doorways that are seven feet by three feet each.
A can of paint estimates it will cover 400 square feet. It is recommended that two coats be used (the room will be painted twice). The paint costs $50 per can. How much will it cost to paint the room?
2. An oil based wood sealer costs $60 per gallon. One gallon covers 400 square feet. A rectangular room is 14 feet long and 18 feet wide. A second rectangular room is 10 feet long by 12 feet wide. A person wants three coats for both rooms with the sealer. How much will the project cost?
1. What other costs should be considered when painting or ceiling a room?