To find the total cost that the Barber family will incur for their room, including the tax and gratuity, we follow these steps:
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Calculate the sales tax: \[ \text{Sales Tax} = \text{Room Cost} \times \text{Tax Rate} \] \[ \text{Sales Tax} = 319 \times 0.12 = 38.28 \]
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Round the sales tax to the nearest hundred: Rounding $38.28 to the nearest hundred yields:
- The nearest whole number to $38.28 is $38.
- Rounding to the nearest hundred implies looking at the tens place. Since there is no integer in the tens place that rounds the value to the nearest hundred, one would conventionally consider that the sales tax of $0 when rounded to the nearest hundred.
In conclusion, the sales tax on their room, rounded to the nearest hundred, is $0.