To calculate the total amount the family of five paid for their dinner, we can break it down into a few steps.
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Calculate the cost of the buffet and drink: The cost per person is $12.80. For five people: \[ \text{Cost for 5 people} = 5 \times 12.80 = 64.00 \]
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Calculate the tax on the bill: The tax rate is 7.5%. First, we calculate the tax amount: \[ \text{Tax} = 64.00 \times 0.075 = 4.80 \]
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Calculate the total amount before gratuity: We add the tax to the initial cost: \[ \text{Total before gratuity} = 64.00 + 4.80 = 68.80 \]
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Calculate the gratuity: The gratuity is 15% of the total before gratuity: \[ \text{Gratuity} = 68.80 \times 0.15 = 10.32 \]
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Calculate the total amount paid: Finally, add the gratuity to the total before gratuity: \[ \text{Total amount paid} = 68.80 + 10.32 = 79.12 \]
Thus, the family ended up paying a total of $79.12.