Question

Three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3. Note: Sales tax is 6%, and tips are rounded to the nearest $0.25. Customer #1: The bill, before sales tax has been added, is $12.95. This customer plans to leave a 15% tip, calculated after the tax has been added. Customer #2: The bill, after sales tax has been added, is $11.65. This customer plans to leave a 20% tip, calculated before the tax was added. Customer #3: The bill, before sales tax has been added, is $11.50. This customer plans to leave an 18% tip, calculated before the tax is added.
1. Which customer has the smallest total bill, including tax and tip?
2. Which of the following expressions best represents the following scenario?
The total bill, b, at a restaurant is first recalculated to include 6% sales tax and then recalculated to include a 16% tip.

a) 1.06b + 0.16(1.06b)
b) b + 0.16(1.06b)
c) 1.06b + 0.16b
d) 1.06(0.16b) + 0.16b

3. Customer #3's total bill is approximately
13%, 11%, 10% 12%
less or more than Customer #1's total bill.

4. Which customer will leave the largest tip?

Answer 1

Customer #2 has the smallest total bill, including tax and tip.
Choice A, 1.06b + 0.16(1.06b), is correct.
Customer 3's bill is approximately 10% less than customer 1's bill.
Customer 2 leaves the bigger tip.

For customer #1:
(1.06(12.95))(1.15) = 15.79; the tip is 0.15(1.06(12.95)) = 2.06.
For customer #2:
1.06x = 11.65; x = 10.99; 20% tip = 0.2(10.99) = 2.20; total = 11.65+2.20 = 13.85.
For customer #3:
1.06(11.50) + 0.18(11.50) = 14.26; the tip is (0.18)(11.50) = 2.07.

Customer 3 spends 15.79-14.26 = 1.53 less than customer #1, which is 1.53/15.79 = 0.097 ≈ 10% less.