Answered

Andrew and Kate have $30 to spend on dinner, tax, and gratuity at Mo's Restaurant. Tax is 6%, and they will give a 15% tip on the total bill after taxes. Their dinner costs $21.00. Which statement correctly explains whether Andrew and Kate have enough money to pay their bill?


AYes. They have enough to pay their bill: $21 \times 1.06 = $22.26 and $22.26 \times 1.15 = $25.60.
BYes. They have enough to pay their bill: $30 \times 1.06 = $31.80 and $31.80 \times 1.15 = $36.57.
CNo. They do not have enough to pay their bill: $21 \times 1.06 = $22.26 and $22.26 \times 1.15 = $25.60.
DNo. They do not have enough to pay their bill: $30 \times 1.06 = $31.80 and $31.80 \times 1.15 = $36.57.

Verified Answer :

  • Calculate the bill after tax by multiplying the dinner cost (\(\$21.00\)) by the tax factor (1.06), which equals \(\$22.26\).
  • Calculate the total cost by multiplying the post-tax bill (\(\$22.26\)) by the tip factor (1.15), resulting in \(\$25.60\).
  • Compare the total cost to the available budget of \(\$30.00\).
  • Since \(\$25.60 \leq \$30.00\), conclude that they have enough money, which corresponds to statement \(\boxed{a}\).

Explanation

  1. Data and Problem Analysis

The problem asks us to determine if Andrew and Kate have enough money to pay for their dinner at a restaurant, given a budget of \(\$30.00\). We are given the following information:

  • Dinner cost: \(\$21.00\).
  • Sales tax rate: \(6\%\), which is \(0.06\).
  • Gratuity (tip) rate: \(15\%\), which is \(0.15\), calculated on the total bill after taxes are added.

Our goal is to calculate the total amount required for the dinner and compare it to their available funds of \(\$30.00\).

  1. Calculating the Bill After Tax

To determine the total cost, we first apply the sales tax to the initial price of the dinner. The tax amount is calculated as:
\[21.00 \times 0.06 = 1.26\]
Adding this tax to the initial cost gives the bill after taxes:
\[21.00 + 1.26 = 22.26\]
Alternatively, this can be calculated as \(21.00 \times 1.06 = 22.26\). Therefore, the bill after tax is \(\$22.26\).

  1. Calculating the Total Bill Including Tip

Next, we calculate the \(15\%\) tip on the bill after tax, which was \(\$22.26\). The tip amount is:
\[22.26 \times 0.15 = 3.339\]
Rounding this to the nearest cent, the tip is \(\$3.34\).
The total bill is the sum of the bill after tax and the tip:
\[22.26 + 3.339 = 25.599\]
Rounded to the nearest cent, the total bill is \(\$25.60\).
Using the multiplication method, we calculate this as:
\[22.26 \times 1.15 = 25.599 \approx 25.60\]
The total cost to pay is \(\$25.60\).

  1. Final Conclusion

Now, we compare the total cost of \(\$25.60\) to the \(\$30.00\) that Andrew and Kate have available.
Since \(\$25.60 \leq \$30.00\), they have enough money to pay for their dinner.
Reviewing the given statements, statement 'a' correctly shows the calculation of the bill after tax (\(21 \times 1.06 = 22.26\)) and the total bill after adding the tip (\(22.26 \times 1.15 = 25.60\)), and it correctly concludes that they have enough money. Therefore, statement 'a' is the correct explanation.

Examples

Calculating a total bill including tax and tips is a common real-life skill needed whenever you dine out. Understanding how percentages work—such as applying a tax rate to the subtotal and a tip rate to that new amount—allows you to accurately manage your budget, plan your expenses before leaving the house, and ensure you can cover the costs of your services. Mastery of these simple algebraic steps helps avoid surprises and ensures responsible financial planning.

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