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Manufacturers will often provide after-purchase rebates to consumers who purchase their product from a retailer as an incentive for consumers to buy their products over competitors products.

House Depot, a large home improvement retailer, has several manufacturer rebate promotions on popular home improvement products during the month of July. In order to qualify for the rebates, one must purchase at least the minimum dollar amount for each product according to the table below.

House Depot Manufacturer Rebates on Select Products

 Floor TilesPaintWallpaper
$50-$100$10None$20
Over $100$20$15$35
Price List for House Depot Home Improvement Products

ProductPackagePrice
Lavertine Tiles1 sq. ft. each
16 per pack
$15
Trinoleum Tiles0.5 sq. ft. each
16 per pack
$10
Magic Color Paint32 sq. ft. worth
per can
$25
Rainbow Wallpaper16 sq. ft. per sheet
10 sheets per pack
$30
Cloud Wallpaper10 sq. ft. per sheet
8 sheets per pack
$32
Packaged products cannot be split into individual products.


TrueFalse 
 The cost of installing Trinoleum Tiles in Marisa's bathroom is $75.
 The pre-rebate cost of 2 coats of Magic Color Paint on the walls of Marisa's bathroom is $500.
 Marisa can cover her walls with Cloud Wallpaper for less than $100.
 The cost of covering the walls with Rainbow wallpaper is greater than the cost of installing Lavertine Tiles
 If she chooses, Marisa can both wallpaper and re-tile her entire bathroom less expensively than she can paint it.

  1. False. The length of each wall is 8 feet, meaning that the square footage of the floor is 8x8 or 64 square feet. Thus, she would need to purchase 8 packs of Trinoleum Tiles, costing $80 before the $10 rebate, so $70 total.
  2. True. Each wall requires 80 square feet of paint (8x10 dimensions per wall), so with four walls she will require 320 square feet of paint total. For two coats, then, she will require 640 square feet. At 32 square feet per can, then she will require 20 cans. 20 cans * $25/can = $500 before the $15 rebate.
  3. True. As discussed in the solution above, she will require 320 square feet of wall covering. Each pack of Cloud Wallpaper provides 80 square feet, so she will require 4 packs at $32 each. Therefore, she will spend $128 before the $35 rebate. Even without doing the pen-and-paper math to arrive at the after-rebate cost of $93, you should quickly be able to note that $128 less a $35 rebate will be less than $100, so the statement is true.
  4. False. Before the rebate, the costs are the same. To cover her floor, she needs to cover 64 square feet (8 feet x 8 feet), so she will require 4 packs of Lavartine tiles at $15/each for a cost of $60. To cover her walls, she will need a total of 320 square feet (4 walls * 8x10 feet per wall), and will therefore require two packs of Rainbow Wallpaper at $30/pack. The pre-rebate cost is thus $60, as well. Only after the $20 rebate on wallpaper and $10 rebate on tile does the cost difference become realized.
  5. True. Wall coverings will require her to purchase 320 square feet's worth, which requires 10 cans of paint at $25/can. That $250 figure is much higher than wallpapering ($60 pre-rebate with Rainbow, the cheaper option) or tiling ($60 pre-rebate with Lavartine, the cheaper option). And because the paint rebate is only $15, one need not do the math to recognize that paint is by far the most expensive option and will not come close to the potential for tile/wallpaper together.