In order to join a yoga club there is a $100 annual fee and a $5 fee for each class you attend. write an equation in slope-intercept form that models this situation.

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

Step-by-step 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 = × 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 = × 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 = × 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 = × 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 = × 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 = × 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 = × 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 + × 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% =

∴ 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)