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?


ANo. They do not have enough to pay their bill:

$\begin{array}{l}

\$ 21 \times 1.06 = \$ 22.26 \text{ and } \\

\$ 22.26 \times 1.15 = \$ 25.60.

\end{array}$


BYes. They have enough to pay their bill:

$\begin{array}{l}

\$ 30 \times 1.06 = \$ 31.80 \text{ and } \\

\$ 31.80 \times 1.15 = \$ 36.57

\end{array}$


CYes. They have enough to pay their bill:

$\begin{array}{l}

\$ 21 \times 1.06 = \$ 22.26 \text{ and } \\

\$ 22.26 \times 1.15 = \$ 25.60

\end{array}$

Verified Answer :

  • Calculate the post-tax bill: \(21.00 \times 1.06 = \$22.26\).
  • Calculate the total bill including the 15% tip: \(22.26 \times 1.15 = \$25.60\).
  • Compare the final bill to the budget: \(\$25.60 < \$30.00\).
  • Since the total bill is less than the available budget, they have enough money. \(\boxed{\text{Yes}}\)

Explanation

  1. Calculating the Final Bill

To determine if Andrew and Kate have enough money, we first calculate the total cost of their dinner including tax and tip.

  1. The initial dinner cost is \(C = \$21.00\).
  2. The tax amount is \(6\%\) of the dinner cost, so the total after tax is \(C \times (1 + 0.06) = 21.00 \times 1.06 = \$22.26\).
  3. The tip is \(15\%\) of the post-tax total, so the final total bill is \(22.26 \times (1 + 0.15) = 22.26 \times 1.15 = \$25.599\), which rounds to \(\$25.60\).
  4. Andrew and Kate have \(\$30\) to spend. Since \(\$25.60 \leq \$30.00\), they have sufficient funds to pay for their meal.
  1. Conclusion and Comparison

The calculations show that the total cost is approximately \(\$25.60\). Comparing this to their budget of \(\$30.00\), we see that they have enough money to cover the bill. None of the provided statements accurately combine the correct math with the correct conclusion; however, the most accurate representation of the cost calculation is \(\$21.00 \times 1.06 = \$22.26\) and \(\$22.26 \times 1.15 = \$25.60\). Thus, Andrew and Kate do have enough money, with a remainder of \(\$30.00 - \$25.60 = \$4.40\). The final answer is that they have enough money.

Examples

This problem demonstrates how to calculate the total cost of a service when taxes and gratuities are applied sequentially. Understanding this process is essential for personal finance, such as budgeting for restaurant visits or online shopping, where additional fees like tax or shipping are applied to a base price before a final payment is made. By breaking down these percentages, one can confidently determine if their planned expenditure fits within their available budget.

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