Mural Wall: Primer, Two Paint Coats, and Whole-Gallon Purchases
A community center is repainting a rectangular mural wall that measures 24 feet long and 9 feet high. The wall has two identical windows, each 3 feet wide and 4 feet high, and one door that is 3 feet wide and 7 feet high; none of these openings will be painted. A gallon of primer covers 400 square feet and costs $29. A gallon of paint covers 300 square feet and costs $38. The center must apply one coat of primer to the entire paintable area and two coats of paint to the same area. Supplies must be bought in whole gallons, and the center has $120 for primer and paint combined. The facilities manager estimates they need about 170 square feet and wants to buy two gallons of paint “just in case.” The volunteer treasurer wants an exact area calculation before approving the purchase, and then asks whether an $8-off coupon on purchases of $75 or more changes the plan.
1. Calculate the exact paintable area of the wall.
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Start with the full rectangular wall: 24 × 9 = 216 square feet. Subtract the two windows: each is 3 × 4 = 12 square feet, so both are 24 square feet. Subtract the door: 3 × 7 = 21 square feet. Paintable area = 216 − 24 − 21 = 171 square feet. The manager’s 170-square-foot estimate is close but slightly low; the exact value matters when checking gallon coverage.
2. How many whole gallons of primer and paint must be purchased, and what is the cost before any coupon?
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Primer covers 400 square feet per gallon and is applied once: 171 ÷ 400 = 0.4275, so 1 gallon is needed. Paint covers 300 square feet per gallon, but two coats are required, so the paint must cover 2 × 171 = 342 square feet. Divide: 342 ÷ 300 = 1.14. Since only whole gallons can be bought, round up to 2 gallons. Cost = 1 × $29 + 2 × $38 = $29 + $76 = $105. This is within the $120 budget, leaving $15.
3. Does the $8-off coupon for purchases of $75 or more apply, and what is the final cost? Would buying only 1 gallon of paint be mathematically sufficient under the stated coverage?
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The pre-coupon total is $105, which is at least $75, so the coupon applies: $105 − $8 = $97 final cost. Buying 1 gallon of paint would cover only 300 square feet, but two coats require 342 square feet, so 1 gallon is not sufficient. The manager’s instinct to buy 2 gallons is correct, but for the precise reason that two coats cover 342 square feet-not because 170 square feet is near a coverage boundary.