To determine which information is not needed to compute the bill after tax and tip, let’s analyze the provided options:
A. The customer left $1.30 as a tip.
B. The tax was 8%.
C. The customer left a 10% tip.
D. All of this information is needed to solve the problem.
The key points are:
- The tax is 8%, which tells us how to calculate the tax on the cost of the meal.
- The tip is 10% of the total after tax, which provides a relationship needed to find the meal cost.
- The specific amount of the tip ($1.30) can be used to calculate the total bill after the tax, but it isn't necessary to know the exact amount since we can derive it from the percentage.
So, option A, "The customer left $1.30 as a tip," is the information that is not needed to compute the total bill directly. We can find the total bill using the tax and the percentage of the tip without knowing the exact dollar amount of the tip itself.
Therefore, the answer to Part 1 is:
A. The customer left $1.30 as a tip.
Now, let's compute the total bill in Part 2.
Let:
- \( C \) = cost of the meal before tax
- Tax = 8% of \( C \)
- Tip = 10% of (Cost + Tax)
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Calculate the tax: \[ \text{Tax} = 0.08C \]
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Calculate the total cost after tax: \[ \text{Total after tax} = C + \text{Tax} = C + 0.08C = 1.08C \]
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Tip based on total after tax:
Given that the tip was $1.30: \[ \text{Tip} = 0.10 \times (1.08C) = 1.30 \] -
Setting up the equation: \[ 0.10 \times (1.08C) = 1.30 \ 0.108C = 1.30 \]
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Solve for \( C \): \[ C = \frac{1.30}{0.108} \approx 12.04 \]
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Calculate the tax amount: \[ \text{Tax} = 0.08 \times 12.04 \approx 0.96 \]
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Total after tax: \[ \text{Total after tax} = 12.04 + 0.96 = 13.00 \]
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Final total bill including tip: \[ \text{Total bill} = \text{Total after tax} + \text{Tip} = 13.00 + 1.30 = 14.30 \]
The total bill, therefore, is approximately $14.30.
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