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.

Question 1-Which customer will leave the largest tip?
Customer #1
Customer #2
Customer #3

Question 2-Which customer has the smallest total bill, including tax and tip?
Customer #1
Customer #2
Customer #3

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

Question4- 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

Answer 1

What the other person said is right.

Explanation:

Answer 2

Question 1: Customer #2 will leave the largest tip

Question 2: Customer #2 has the smallest total bill, including tax and tip

Question 3: Customer #3's total bill is approximately 10% less than Customer #1's total bill

Question 4: The best expression represents the scenario is 1.06 b + 0.16(1.06 b) ⇒ a

Explanation:

Let us solve it step by step

Customer #1:

∵ The bill, before sales tax has been added, is $12.95

∵ The sales tax is 6%

- Multiply 6% by the 12.95 to find the sales tax amount

∴ The sales tax =
`(6)/(100)` × 12.95 = $0.777

- Add it the bill

∴ The bill after the sales tax = 12.95 + 0.777 = $13.727

∵ He plans to leave a 15% tip, calculated after the tax has been added

- Multiply 15% by 13.727 to find the tips

∴ The tips =
`(15)/(100)` × 13.727 = $2.06

- Now add the tips to the bill after sales tax

∴ The total bill = 13.73 + 2.06 = $15.79

Customer #2:

∵ The bill, after sales tax has been added, is $11.65

∵ The sales tax is 6%

- Multiply 6% by the 11.65 to find the sales tax amount

∴ The sales tax =
`(6)/(100)` × x = 0.06 x where x is the bill before tax

- Equate the sum of x and 0.06 x by 11.65

∴ x + 0.06 x = 11.65

∴ 1.06 x = 11.65

- Divide both sides by 1.06

∴ x = 10.99

∴ The bill before sales tax = $10.99

∵ He plans to leave a 20% tip, calculated before the tax was added

- Multiply 20% by 10.99 to find the tips

∴ The tips =
`(20)/(100)` × 10.99 = $2.20

- Now add the tips to the bill after sales tax

∴ The total bill = 11.65 + 2.20 = $13.85

Customer #3:

∵ The bill, before sales tax has been added, is $11.50

∵ The sales tax is 6%

- Multiply 6% by the 11.50 to find the sales tax amount

∴ The sales tax =
`(6)/(100)` × 11.50 = $0.69

- Add it the bill

∴ The bill after the sales tax = 12.95 + 0.777 = $13.727

∵ He plans to leave a 18% tip, calculated before the tax is added

- Multiply 18% by 11.50 to find the tips

∴ The tips =
`(18)/(100)` × 11.50 = $2.07

- Now add the tips, the tax to the bill

∴ The total bill = 11.50 + 2.07 + 0.69 = $14.26

Now lets answer the questions

Question 1:

∵ Customer #1 will leave $2.06

∵ Customer #2 will leave $2.20

∵ Customer #3 will leave $2.07

∴ Customer #2 will leave the largest tip

Question 2:

∵ Customer #1's total bill is $15.79

∵ Customer #2's total bill is $13.85

∵ Customer #3's total bill is $14.26

∴ Customer #2 has the smallest total bill, including tax and tip

Question 3:

∵ Customer #3's total bill is $14.26

∵ Customer #1's total bill is $15.79

- Find the difference between them

∵ 15.79 - 14.26 = 1.53

∴ Customer #3 is less than Customer #1 by $1.53

- Find the percentage of 1.53 from the Customer #1

∵ The percentage =
`(1.53)/(15.79)` × 100% = 9.69% ≅ 10%

∴ Customer #3's total bill is approximately 10% less than Customer #1's total bill

Question 4:

∵ The total bill is b

∵ It is first recalculated to include 6% sales tax

∴ The bill after the tax = b + 6% of b

∴ The bill after the tax = b +
`(6)/(100)` × b

∴ The bill after the tax = b + 0.06 b

∴ The bill after the tax = 1.06 b

∵ It is recalculated to include a 16% tip

- That means add 16% of b to 1.06 b

∴ The bill after the tip = 1.06 b + 16% of 1.06

∴ The bill after the tip = 1.06 b + 16% × 1.06

∵ 16% =
`(16)/(100)`

∴ The bill after the tip = 1.06 b + 0.16(1.06 b)

∴ The best expression represents the scenario is 1.06 b + 0.16(1.06 b)