Question

You are remodeling your bedroom. You will paint all 4 walls and the door. There are no windows in the room. The floor is 9' by 14' and the walls are 8' tall. (1) What is the area of all 4 walls together? 4032 sq. ft. If a gallon of paint covers 350 sq. ft., (2) how many gallons will you have to buy? (remember you can't buy .4 of a gallon) gallons. (3) How many gallons will it take to put on 2 coats of paint? gallons (4) If the paint costs $25 per gallon, and you are applying 2 coats of paint, how much will you spend on paint? $ Flooring: (5) What is the area of the floor? sq. ft. Oak Flooring costs $6.75 per square foot and Maple costs $8.00 per square foot while carpet costs 3.75 per square foot. (6) What is the cost to redo the floor in oak? $ (7) What is the cost to redo the floor in maple? $ (8) What is the cost to redo the floor in carpet? $

Answer 1

Part 1) The area of the 4 walls is
`368\ ft^2`

Part 2) You will have to buy 2 gallons

Part 3) You will have to buy 3 gallons

Part 4)
`\$75`

Part 5) The area of the floor is
`126\ ft^2`

Part 6)
`\$850.5`

Part 7)
`\$1,008`

Part 8)
`\$472.5`

Explanation:

Part 1) What is the area of all 4 walls together?

we know that

The area of all 4 walls together is equal to the perimeter of the floor multiplied by the height of the wall (8 ft)

so

The perimeter of the floor is

`P=2(9+14)=46\ ft`

The area of the walls is

`46(8)=368\ ft^2`

Part 2) If a gallon of paint covers 350 sq. ft., How many gallons will you have to buy?

using proportion

`(1)/(350)\ (gal)/(ft^2)=(x)/(368)\ (gal)/(ft^2)\\\\x=368/350\\\\x=1.05\ gal`

Remember that you can't buy a fraction of gallon

so

You will have to buy 2 gallons

Part 3) How many gallons will it take to put on 2 coats of paint?

Now the area will be

`368(2)=736\ ft^2`

using proportion

`(1)/(350)\ (gal)/(ft^2)=(x)/(736)\ (gal)/(ft^2)\\\\x=736/350\\\\x=2.10\ gal`

Remember that you can't buy a fraction of gallon

so

You will have to buy 3 gallons

Part 4) If the paint costs $25 per gallon, and you are applying 2 coats of paint, how much will you spend on paint?

To find the cost multiply the number of gallons by $25 per gallon

so

`3(25)=\$75`

Part 5) What is the area of the floor?

The area of the floor (rectangle ) is equal to multiply the length of the floor by the width of the floor

`A=(9)(14)=126\ ft^2`

Part 6) What is the cost to redo the floor in oak?

To find the cost multiply the area of the floor by $6.75 per square foot

so

`126(6.75)=\$850.5`

Part 7) What is the cost to redo the floor in maple?

To find the cost multiply the area of the floor by $8.00 per square foot

so

`126(8.00)=\$1,008`

Part 8) What is the cost to redo the floor in carpet?

To find the cost multiply the area of the floor by $3.75 per square foot

so

`126(3.75)=\$472.5`