A restaurant customer left ​$1.40 as a tip. The tax was 7 % and the tip was 20​% of the cost including tax.

Question

a. Which information is not needed to compute the bill after tax and​ tip?
b. What was the total​ bill?
Question content area bottom
Part 1
a. Which information is not needed to solve this​ problem?
A.
The customer left a 20​% tip.
B.
The tax was 7​%.
Your answer is correct.C.
The customer left ​$1.40 as a tip.
D.
All of this information is needed to solve the problem.
Part 2
b. The total bill is ​$
  
enter your response here.

Answer 1

To solve the problem, let's break it down step by step.

Part 1

Which information is not needed to solve this problem?

The answer is C. The customer left $1.40 as a tip.

This is because, while we can calculate the original bill before tax and tip using the tip amount, we do not need the specific dollar amount of the tip to find the total bill. We only need to know the percentages of tax and tip.

Part 2

What was the total bill?

Let's denote the original bill (before tax) as \( B \).

1. The tax is 7%, so the tax amount is \( 0.07B \).

2. The total after tax is \( B + 0.07B = 1.07B \).

3. The tip is 20% of the total after tax, which means the tip can be expressed as:

   \[ \text{Tip} = 0.20 \times (1.07B) = 0.214B \]

4. We know that the tip amount is $1.40, so we can set up the equation:

   \[ 0.214B = 1.40 \]

5. Now, solve for \( B \):

   \[ B = \frac{1.40}{0.214} \approx 6.54 \text{ (original bill before tax)} \]

6. Now calculate the total bill after tax:

   \[ \text{Total bill after tax} = 1.07B = 1.07 \times 6.54 \approx 6.99 \]

7. Finally, add the tip to the total bill after tax:

   \[ \text{Total bill} = 6.99 + 1.40 \approx 8.39 \]

Therefore, the total bill is approximately $8.39.

Final Answer: The total bill is $8.39.