Question

Let's pretend you have just received a check for $1,500 from a long-lost relative. With this money, you decide that you would like to remodel a room in your home. The room measures 16 feet 6 inches in width by 19 feet 3 inches in length. The height of the ceiling is 8 feet 9 inches. Your plan is to paint every wall and ceiling and buy new carpet for the floor. Assume that there are no doors or windows for ease of calculation.

Convert the length, width, and height measurements to fractional form. Be sure to reduce your fractions.
Convert the fractions you obtained in question 1 into decimals.
Calculate the square footage of your floor.
The carpet comes in rolls of 36 square feet. Calculate how many rolls of carpet will be needed.
Carpet costs $82 per roll. Calculate the cost of the new carpet.
Calculate the total surface area of each wall and ceiling.
Before you paint your walls and ceiling, you decide that you want to use a layer of primer. If a gallon of primer covers 100 square feet, calculate how many gallons of primer you will need to purchase.
A gallon of paint will cover 150 square feet. Calculate how many gallons of paint you will need to purchase to cover each wall and ceiling.
If the primer costs $49.95 per gallon, calculate the cost of the primer needed to cover the walls and ceiling.
If the paint costs $59.95 per gallon, calculate the cost of the paint needed to paint the walls and ceiling.
Calculate the total cost of materials for this project.
Apply a 6% sales tax on the total obtained in question 11.
Questions:
Were you able to come in under budget? If not, how would you be able to modify your plans?
What did you enjoy most about this activity?
How did this activity connect to the weekly material?
Are there any hints or reminders you would provide your fellow classmates if they were to attempt the same activity using an actual room in there home?

Answer 1

Question 1: To convert 16'6", 19'3" and 8'9" to fractional form, you use the fact that 1 foot = 12 inches. Starting with 16'6", there are 16 whole inches + 6/12 of an inch, so the fraction as a mixed number is 16 6/12. To reduce, find the highest common factor between the numerator and the denominator (6) and divide both sides by that number. The resulting fraction is 16 1/2. To convert to an improper fraction, multiply the whole by the denominator (16x2=32) and add the numerator (32+1=33). The denominator stays the same. It is 33/2. Do the same with 19'3" (19 3/12→19 1/4→77/4), and 8'9" (8 9/12→8 3/4→35/4)

Answer: width = 33/2', length = 77/4', height = 35/4'.

To convert to decimals, you do a simple division calculation with each of them. 33/2 = 16.5, 79/4 = 19.25 and 35/4 = 8.75. Don't forget the units.

Question 2: The square footage of the floor is length x width (16.5'x19.25'), which is 317.625 square feet.

Answer: 317.625ft²

Question 3: To calculate the amount of rolls needed, divide the square footage of the room by that of the carpet. 317.625/36 = 8.82291667. Since we want a whole number, round up to 9.

Answer: 9 rolls

Question 4: To calculate the total cost, multiply the amount by the cost of each individual carpet. 9x82 = 738. Don't forget the units.

Answer: $738.00

Question 5: To calculate the surface area of the walls and ceiling, work out length x height and width x height. Since this is a rectangular room (I presume), you only need to do 2 calculations since opposite walls will have the same surface area. 16.5x8.75 = 144.375 and 19.25x8.75 = 168.4375. Since the surface area of the ceiling is the same as that of the floor, you don't need to do any calculations. It is 317.625ft²

Answer: Small wall = 144.375ft², large wall = 168.4375ft², ceiling = 317.625ft²

Question 6: To calculate the amount of primer, you first need to calculate the total surface area of all the walls and ceiling. 2x144.375 + 2x168.4375 + 317.625 = 943.25. Each gallon covers 100sq ft. This can be written as a fraction like so: 1/100. Now, you must multiply both sides of the fraction so that the denominator equals 943.25. You can easily find what to multiply by by calculating 943.25/100. This equates to 9.4325. Therefore, the numerator will also become 9.4325. So you will need to buy 10 gallons of primer.

Answer: 10 gallons of primer

Question 7: To calculate the amount of paint, repeat the process in Q6, but the fraction is 1/150. Multiply both sides of the fraction so that the denominator equals 943.25. 943.25/150 equates to a little bit over 6 gallons. Therefore, the numerator will also become a little over 6. So you will need to buy 7 gallons of paint.

Answer: 7 gallons of paint

Question 8: To calculate the cost of the primer and the paint, multiply the price per gallon by gallons needed (the reason this works is because price ÷ gallon x gallon simplifies to just price :) ). 10x49.95 = 499.5 and 7x59.95 = 419.65. Don't forget units.

Answer: Price of primer = $499.50, price of paint = $419.65.

Question 9: 499.5 + 419.65 + 738 = 1657.15. Don't forget units.

Answer: $1657.15

Question 10: I assume question 11 in the question is question 9 in my answer. To apply a 6% sales tax, find 6% of the total cost and add it to the total cost. 6% is equivalent to 0.06. 0.06x1657.15 = 99.429. 1657.15+99.429 = 1756.579. Round up to 1756.58. Don't forget units.

Answer: $1756.58

Answers to final questions:

• No, the cost was too high
• You could scrap the carpet or the paint or the primer.
• The final questions are for you to answer.

I worked these out with the data I was given. I hope this helps.