To calculate the tax rate on Mrs. Torres' meals, we first need to determine the total costs associated with her hotel stay and meals.
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Hotel Charges:
- Room charge for 3 nights = 3 nights * $80/night = $240
- Hotel tax (9%): \( 0.09 \times 240 = 21.60 \)
- Tip for maid service (10%): \( 0.10 \times 240 = 24.00 \)
Total cost for hotel stay: \[ 240 + 21.60 + 24 = 285.60 \]
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Meal Charges:
- Meal cost before tax = $109.30
- Tip for meals (15%): \( 0.15 \times 109.30 = 16.395 \)
Total cost for meals (including tip): \[ 109.30 + 16.395 = 125.695 \]
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Total Trip Cost:
- Total calculated cost up until now: \[ 285.60 + 125.695 = 411.295 \]
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Difference to Total Cost:
- Given total cost = $420.04
- Difference (which accounts for the meals tax): \[ 420.04 - 411.295 = 8.745 \]
To find the tax rate on the meals, we first need to confirm that this amount represents the meal tax and then find out what that tax rate is.
The tax on meals is assumed to be the total tax amount:
- Let the meal tax be represented as \( x \).
- The total meal amount (including meals before tax, tax, and tip) is \( 109.30 + x + 16.395 = 125.695 + x \)
We already know that this should sum up to: \[ 125.695 + x = 125.695 + \text{tax} \] Thus: \[ x = \text{tax} \]
Setting \( x \) as a proportion of the pre-tax meal charge:
- The tax on the meals can be expressed as \( \text{meal tax} = (109.30) \cdot r \), where \( r \) is the tax rate.
We have: \[ 0.09 \times 109.30 \quad (for accuracy) \]
Putting this together, we have: \[ x = 8.745 \] This equation represents the tax calculation. To find the tax rate on the meals: \[ \frac{8.745}{109.30} = r \] Calculating \( r \): \[ = \frac{8.745}{109.30} \approx 0.0799 \text{ or } 7.99% \]
This value is most closely represented by 8%.
Thus, the approximate tax rate Mrs. Torres pays on her meals is: \[ \text{Answer: } c. 8% \]