Question

3. The Fergusons decided to book the room at the price that Mrs. Ferguson was given, $2075, because it included breakfast for both of them for the entire stay. The travel agent could not match that price. At the end of the trip, Mr. Ferguson received a bill showing a pre-tax amount of $2075. The tax is 18.5%. When the Fergusons went to check out, they told the front desk that the refrigerator in the room had not worked during the majority of their time there. The hotel decided to give them a 15% discount off the pre-tax amount. Mr. Ferguson says the new total will be $2147.63. He shows Mrs. Ferguson how he found the new total. Since we have to add 18.5% tax and subtract 15% for the discount, this means we will add 3.5% in the end. Your Score ___ of 20 18.5 – 15 = 3.5 Therefore, we just need to multiply the cost of the room by 3.5% and add this number to the cost of the room to determine what we owe. 3.5% • 2075 = 0.035 • 2075 = 72.625, which rounds to $72.63 Add $72.63 to the total $2075 to get $2147.63. Explain why Mr. Ferguson’s calculations are incorrect. What is the correct total? Show two ways to solve this problem. Remember that businesses typically round money amounts up, so round your answer to the next highest cent if necessary.

Answer 1

Given:
Pre-tax amount: 2,075
Tax is 18.5%
Discount on Pre-tax amount: 15%

We should first compute for the discount before the tax.
2,075 * 15% = 311.25
2,075 - 311.25 = 1763.75

Tax paid based on discounted pre-tax amount
1,763.75 * 18.5% = 326.29
1,763.75 + 326.29 = 2,090.04

Total discount :    311.25
Total tax           :    326.29
Total amt. paid: 2,090.04

Mr. Ferguson's calculation is incorrect because both rates have different bases. The base of the discount is the pretax amount, while the base of the tax rate is the pretax amount, net of the discount.

Each rate should be applied individually to the amount, not deducted from each other with the difference applied to one base amount.