To determine which information is not needed to compute the bill after tax and tip, let's analyze the options provided:
A. The customer left a 15% tip. - This is needed to calculate the tip based on the total cost after tax.
B. The tax was 6%. - This is needed to calculate the tax amount based on the initial cost of the meal.
C. The customer left $1.05 as a tip. - This is directly used to find the total bill since we need to solve for the original cost based on this information.
D. All of this information is needed to solve the problem. - This implies none of the information is unnecessary.
Given the context, the answer is not D. Each individual piece of information is necessary for solving the problem:
- The percentage for the tip is needed to determine how much of an increase the tip provides to the total bill.
- The tax percentage is needed to calculate how much tax needs to be added to the meal cost.
- The dollar amount of the tip ($1.05) is necessary to determine the size of the original meal cost from which we can backtrack to find the total bill.
Thus, the correct answer is: D. All of this information is needed to solve the problem.
Part 2: To calculate the total bill, we need to derive it as follows:
Let's denote the original bill before tax as \( x \).
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Calculate tax: \[ \text{Tax Amount} = 0.06x \]
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Total bill including tax: \[ \text{Total after tax} = x + 0.06x = 1.06x \]
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Calculate the tip based on the total after tax: \[ \text{Tip} = 0.15 \times (1.06x) = 0.159x \]
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Given that the tip is $1.05: \[ 0.159x = 1.05 \]
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Solve for \( x \): \[ x = \frac{1.05}{0.159} \approx 6.60 \]
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Now we can find the total bill: \[ \text{Total Bill} = 1.06x = 1.06 \times 6.60 \approx 6.99 \]
Finally, the total bill is approximately $6.99. Adding the tax and tip gives you the total amount paid.
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