MATH SOLVE

4 months ago

Q:
# 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 + 0.16bd) 1.06(0.16b) + 0.16b3. 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?

Accepted Solution

A:

Answer:Question 1: Customer #2 will leave the largest tipQuestion 2: Customer #2 has the smallest total bill, including tax and tipQuestion 3: Customer #3's total bill is approximately 10% less than Customer #1's total billQuestion 4: The best expression represents the scenario is 1.06 b + 0.16(1.06 b) ⇒ aStep-by-step explanation:Let us solve it step by stepCustomer #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 = [tex]\frac{6}{100}[/tex] × 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 = [tex]\frac{15}{100}[/tex] × 13.727 = $2.06- Now add the tips to the bill after sales tax∴ The total bill = 13.73 + 2.06 = $15.79Customer #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 = [tex]\frac{6}{100}[/tex] × 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 = [tex]\frac{20}{100}[/tex] × 10.99 = $2.20- Now add the tips to the bill after sales tax∴ The total bill = 11.65 + 2.20 = $13.85Customer #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 = [tex]\frac{6}{100}[/tex] × 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 = [tex]\frac{18}{100}[/tex] × 11.50 = $2.07- Now add the tips, the tax to the bill ∴ The total bill = 11.50 + 2.07 + 0.69 = $14.26Now lets answer the questionsQuestion 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 tipQuestion 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 tipQuestion 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 = [tex]\frac{1.53}{15.79}[/tex] × 100% = 9.69% ≅ 10%∴ Customer #3's total bill is approximately 10% less than Customer #1's total billQuestion 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 + [tex]\frac{6}{100}[/tex] × 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% = [tex]\frac{16}{100}[/tex]∴ 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)