Question

3 - 101, mr. wallis is back!
after much consideration, mr. wallis decided to use the tip table below to help him estimate what a 15% tip would be for various costs of dinner.

cost of dinner	$10	$20	$30	$35	$40	$45	$50	$100
amount of tip	$1.50	$3	$4.50	$5.25	$6	$6.75	$7.50	$15

a. find a rule for his table. that is, find a rule that calculates the amount of tip (y) based on the cost of the dinner (x).
b. after dinner, mr. wallis was so distracted that he forgot to write down the cost of the meal in his check - book. all he remembers is that he left a $9 tip. what was the original cost of the meal before he paid the tip? use your equation from part (a) to answer this question.
what was the total cost of the meal including the tip?
what would his bill be if he left a $12 tip? what was the total cost of the meal including the tip?
what would his bill be if he left a $9.75 tip? what was the total cost of the meal including the tip?

Explanation:

Step1: Identify the relationship

Since it's a 15% tip, the rule is $y = 0.15x$, where $y$ is the tip amount and $x$ is the cost of dinner.

Step2: Find cost of meal for $9 tip

Set $y = 9$ in $y=0.15x$. Then $x=\frac{y}{0.15}=\frac{9}{0.15}=60$.

Step3: Find total cost for $9 tip

Total cost = cost of meal + tip = $60 + 9=69$.

Step4: Find cost of meal for $12 tip

Set $y = 12$ in $y = 0.15x$. Then $x=\frac{y}{0.15}=\frac{12}{0.15}=80$. Total cost = $80+12 = 92$.

Step5: Find cost of meal for $9.75 tip

Set $y = 9.75$ in $y = 0.15x$. Then $x=\frac{y}{0.15}=\frac{9.75}{0.15}=65$. Total cost = $65 + 9.75=74.75$.

Answer:

a. $y = 0.15x$
b. Cost of meal before tip for $9 tip: $60
Total cost of meal including $9 tip: $69
Cost of meal before tip for $12 tip: $80
Total cost of meal including $12 tip: $92
Cost of meal before tip for $9.75 tip: $65
Total cost of meal including $9.75 tip: $74.75