Originally, the bill for Quon's meal was $11.88, which included an 8% tax on the cost of the meal. Quon...

1. Translate the problem requirements: We need to work backwards from the original bill to find the meal cost, apply the \(25\%\) discount, then calculate the new bill with \(8\%\) tax on the discounted amount
2. Find the original meal cost before any tax: Work backwards from \(\$11.88\) which includes \(8\%\) tax to find the base meal cost
3. Apply the discount to the original meal cost: Calculate \(25\%\) off the original meal cost to get the discounted meal cost
4. Calculate the final bill with tax on discounted amount: Add \(8\%\) tax to the discounted meal cost to get Quon's final bill

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what's happening in plain English:

• Quon got a meal that cost some amount (we don't know this yet)
• The restaurant added \(8\%\) tax to that meal cost
• After adding tax, his bill was \(\$11.88\)
• Then Quon used a \(25\%\) off coupon on just the meal cost (not the total bill)
• The restaurant calculated a new bill: discounted meal cost + \(8\%\) tax on that discounted amount

We need to find this final bill amount.

Process Skill: TRANSLATE - Converting the word problem into a clear sequence of mathematical operations

2. Find the original meal cost before any tax

We know that:
Original meal cost + \(8\%\) tax on that cost = \(\$11.88\)

Let's think about this step by step. If the meal cost was some amount, and we add \(8\%\) tax to it, we get the total bill.

In everyday terms: If something costs \(\$100\) and we add \(8\%\) tax, we pay \(\$108\) total.
So the total bill is \(108\%\) of the original cost, or \(1.08\) times the original cost.

Here: \(\mathrm{Original\,meal\,cost} \times 1.08 = \$11.88\)

To find the original meal cost:
\(\mathrm{Original\,meal\,cost} = \$11.88 \div 1.08 = \$11.00\)

Let's verify: \(\$11.00 + (8\% \text{ of } \$11.00) = \$11.00 + \$0.88 = \$11.88\) ✓

3. Apply the discount to the original meal cost

Now we apply the \(25\%\) discount to the original meal cost of \(\$11.00\).

\(25\%\) off means Quon pays \(75\%\) of the original price.
\(75\% \text{ of } \$11.00 = 0.75 \times \$11.00 = \$8.25\)

So the discounted meal cost is \(\$8.25\).

4. Calculate the final bill with tax on discounted amount

Now we need to add \(8\%\) tax to this discounted meal cost of \(\$8.25\).

Just like before, when we add \(8\%\) tax to something, we multiply by \(1.08\):
\(\mathrm{Final\,bill} = \$8.25 \times 1.08\)

Let's calculate this step by step:
\(8\% \text{ of } \$8.25 = 0.08 \times \$8.25 = \$0.66\)
\(\mathrm{Final\,bill} = \$8.25 + \$0.66 = \$8.91\)

Final Answer

Quon's final bill was \(\$8.91\).

This matches answer choice A: \(\$8.91\).

Common Faltering Points

Errors while devising the approach

1. Misunderstanding what the discount applies to: Students often think the \(25\%\) discount applies to the entire \(\$11.88\) bill (including tax) rather than just the original meal cost. This leads them to calculate \(25\% \text{ off } \$11.88 = \$8.91\), then add tax, getting an incorrect final answer.

2. Confusion about the tax calculation sequence: Students may not realize they need to first remove the original tax to find the base meal cost, then apply the discount, then recalculate tax on the discounted amount. They might try to apply the discount directly without properly handling the tax components.

3. Misinterpreting 'final bill' requirements: Some students might calculate only the discounted meal cost (\(\$8.25\)) and forget that the final bill must include the \(8\%\) tax on this discounted amount.

Errors while executing the approach

1. Incorrect percentage calculations: When finding the original meal cost, students might divide by \(0.08\) instead of \(1.08\), or when applying the \(25\%\) discount, they might multiply by \(0.25\) instead of \(0.75\).

2. Arithmetic errors in tax calculations: Students may miscalculate \(8\% \text{ of } \$8.25\) as \(\$0.68\) instead of \(\$0.66\), leading to a final answer of \(\$8.93\) instead of \(\$8.91\). This is a particularly common error due to the decimal multiplication.

3. Rounding errors during intermediate steps: Students might round the original meal cost to something other than the exact \(\$11.00\), which would propagate errors through the remaining calculations.

Errors while selecting the answer

1. Selecting the discounted meal cost instead of final bill: Students who correctly calculate the discounted meal cost as \(\$8.25\) but forget to add the tax might look for this value among the choices, potentially selecting the closest option.

2. Choosing the result of incorrect discount application: Students who applied the \(25\%\) discount to the full \(\$11.88\) bill and then added tax would get \(\$8.91 + \text{tax} \approx \$9.62\), leading them to select choice D instead of recognizing that \(\$8.91\) is actually the correct final answer.