Question

Spencer visits an electronics store to buy a tablet. The store is having a sale and discounting all tablets by 15% of the marked price. He buys a tablet with a marked price of $214.80.

Part A: Set up a proportion that can be used to find the dollar amount of the discount (d).

Part B: Given that the sales tax in Spencer's state is 6%, what is the final cost of the tablet Spencer buys?

Part C: Spencer's sister, Laura, lives in a different state with an 8% sales tax rate. Laura found the same tablet discounted 30% from a regular price of $226.50. If Laura buys the tablet, who pays the lower total cost? Justify your answer.​

Answer 1

Part A: To find the discount, set up a proportion using the marked price and the dollar amount of the discount. Part B: Subtract the discount amount and add the sales tax to find the final cost of the tablet. Part C: Calculate the total cost for Laura by subtracting the discount and adding the sales tax to determine who pays the lower total cost.

Step-by-step explanation:

Part A: To set up a proportion to find the dollar amount of the discount (d), we can use the following equation:

x/100 = d/214.80

Where x represents the percentage discount. Since the discount is 15%, we can substitute x with 15:

15/100 = d/214.80

Simplifying the equation, we get:

d = (15/100) * 214.80

d = 32.22

Therefore, the dollar amount of the discount is $32.22.

Part B: To find the final cost of the tablet Spencer buys, we need to subtract the discount amount and add the sales tax. The final cost can be calculated as:

Final cost = Marked price - Discount + Sales tax

Final cost = 214.80 - 32.22 + (6/100) * (214.80 - 32.22)

Final cost = 182.58 + (6/100) * 182.58

Final cost = 182.58 + 10.95

Final cost = 193.53

Therefore, the final cost of the tablet Spencer buys is $193.53.

Part C: To compare the total cost for Laura, we need to calculate the discount and add the sales tax. The total cost for Laura can be calculated as:

Total cost = Regular price - Discount + Sales tax

Total cost = 226.50 - 0.30 * 226.50 + (8/100) * (226.50 - 0.30 * 226.50)

Total cost = 226.50 - 0.30 * 226.50 + (8/100) * 226.50 - (8/100) * 0.30 * 226.50

Total cost = 226.50 - 0.30 * 226.50 + 0.08 * 226.50 - 0.08 * 0.30 * 226.50

Total cost = 226.50 - 0.30 * 226.50 + 0.08 * 226.50 - 0.08 * 0.30 * 226.50

Total cost = 226.50 - 67.95 + 0.08 * 226.50 - 0.0216 * 226.50

Total cost = 226.50 - 67.95 + 18.12 - 4.8974

Total cost = 171.63 + 13.22

Total cost = 184.85

Therefore, Spencer pays the lower total cost of $193.53 compared to Laura's $184.85.