282,221 views
22 votes
22 votes
A gym at a school is being painted. The four walls and the ceiling are to be painted (but not the floor). The gym measures 100 ft x 65 ft x 25 ft. A 5 gallon can of paint costs $151.99 and covers 1750 ft. How many cans should be purchased? What will it cost to paint two coats for this gym (include HST)? ​

User Tavison
by
2.3k points

2 Answers

15 votes
15 votes

Final answer:

To paint the gym's walls and ceiling with two coats of paint, 18 cans of paint are needed, costing a total of $3,091.48 including a 13% HST.

Step-by-step explanation:

To determine the number of paint cans needed to paint the gym, we first calculate the total surface area to be painted. The gym has four walls and a ceiling, and we are given that the gym's dimensions are 100 ft (length) x 65 ft (width) x 25 ft (height). The floor won't be painted.

The total surface area of the walls is given by the formula for the perimeter of the base multiplied by the height, which is 2 × (length + width) × height. This leads to 2 × (100 ft + 65 ft) × 25 ft = 2 × 165 ft × 25 ft = 8,250 square feet for the walls. The area of the ceiling is length times width, which is 100 ft * 65 ft = 6,500 square feet.

Thus, the total area to be painted for one coat is 8,250 ft + 6,500 ft = 14,750 square feet. Since each can cover 1,750 square feet, we divide the total area needed by the coverage per can: 14,750 ft / 1,750 ft/can = 8.43 cans. Since we cannot purchase a fraction of a can, we round up to 9 cans per coat.

For two coats, we need twice the number of cans, so 9 cans × 2 = 18 cans. The cost per can is $151.99, so cost for 18 cans is 18 × $151.99 = $2,735.82 before tax.

To include the Harmonized Sales Tax (HST), we multiply by the HST rate, assuming it is 13%, thus total cost with HST is $2,735.82 × 1.13 = $3,091.48.

User Ronald Randon
by
2.9k points
18 votes
18 votes

9514 1404 393

Answer:

  • 17 cans
  • $2,971.40

Step-by-step explanation:

We assume ...

  • the 25' dimension is the wall height
  • the HST rate is 15% (the paint is not purchased in Ontario)
  • only full cans of paint can be purchased

The wall area is the wall height times the perimeter of the room.

wall area = (25')(2(100' +65')) = 8250 ft²

The ceiling area is the product of length and width.

ceiling area = (100')(65') = 6500 ft²

Then the area to be painted with each coat is ...

painted area = wall area + ceiling area = (8250 +6500) ft² = 14750 ft²

Then two coats of paint will require sufficient paint to cover ...

(2 coats)×(14750 ft²/coat) = 29,500 ft²

__

If each can of paint covers 1750 ft², the number of cans required is ...

(29,500 ft²)/(1750 ft²/can) = 16.86 cans

17 cans must be purchased

__

The cost of 17 cans of paint with sales tax will be ...

(17 cans)($151.99/can)(1 +15%) = $2971.40

User Lucas Holt
by
2.4k points