Math Problem Statement

A restaurant customer left $0.90 as a tip. The tax was 4% and the tip was 10% of the after-tax cost. Which information is not needed to compute the bill after tax and tip? What was the total bill?

Solution

To solve this problem, let's break down the information given and identify what is necessary to determine the total bill amount.

  1. Information Provided:

    • The customer left $0.90 as a tip.
    • The tax was 4%.
    • The tip was 10% of the after-tax cost.
  2. Key Question:

    • Which information is not needed to compute the bill after tax and tip?
  3. Analysis:

    • Since the tip is given as $0.90, and this amount represents 10% of the after-tax cost, we can use this information directly to find the after-tax cost.
    • Let the after-tax amount be xx. Then, 10% of xx (which is 0.10x0.10x) should equal $0.90.
    • Solving for xx, we get: 0.10x=0.900.10x = 0.90 x=0.900.10=9.00x = \frac{0.90}{0.10} = 9.00
    • So, the after-tax cost is $9.00.
    • To find the original bill before tax, we know that the tax is 4%, so the original amount (before tax) is calculated as follows: Original amount=9.001.04=8.65 (approximately)\text{Original amount} = \frac{9.00}{1.04} = 8.65 \text{ (approximately)}
  4. Determining Which Information is Unnecessary:

    • Since we do not need the specific tax rate of 4% to determine the tip (only the amount of $0.90 was needed), option A ("The tax was 4%.") is the correct answer for the information that is not needed.
  5. Total Bill Calculation:

    • The total bill after tax and tip is: 9.00+0.90=9.909.00 + 0.90 = 9.90
    • So, the total bill is $9.90.

Would you like further details or explanations on any part of this solution?


Here are some related questions to deepen your understanding:

  1. How would the total change if the tax was 5% instead of 4%?
  2. If the customer had left a different tip amount, say $1.00, how would the calculations change?
  3. Why is the tax percentage irrelevant for determining the total bill?
  4. Can we calculate the before-tax amount using only the tip percentage and tip amount?
  5. How would the solution differ if the question asked for the original bill amount without any tax?

Tip: When given percentages in problems, identify which values directly affect the calculations and which ones might be extraneous for the solution.

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Math Problem Analysis

Mathematical Concepts

Percentages
Basic Algebra

Formulas

Tip calculation formula: Tip Amount = Percentage × Cost
Total Bill calculation: After-tax Cost + Tip Amount

Theorems

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Suitable Grade Level

Grades 6-8