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.