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Difficulty: MediumTaxes and Tips

A group of friends goes out for dinner. The total bill comes to $74.40, which includes a 6% sales tax and an 18% tip. If both the tax and the tip were calculated based on the original cost of the food, what was the cost of the food before the tax and tip were added?

Answer:The original cost of the food was $【60】.

Answer

The original cost of the food was $60.00.
By adding the 6% sales tax and the 18% tip, we find that a total of 24% was added to the original cost. This means the final bill of 74.40isequalto12474.40 is equal to 124% (or 1.24 times) the original food cost. Dividing 74.40 by 1.24 gives the correct original cost of $60.00.

Step-by-Step Solution

1
Determine the combined percentage rate applied to the original cost.
Combined percentage = 6% tax + 18% tip = 24%.
Since both the tax and the tip are based on the original food cost, their percentages can be added together.
2
Express the total bill as a percentage of the original cost.
The total bill represents 100% of the original cost plus the 24% in additions, which equals 124% of the original cost.
The final amount includes the original base amount (100%) and the additional charges.
3
Set up an equation and solve for the original cost.
Let x be the original cost. 1.24x = $74.40. Dividing both sides by 1.24 gives x = 60.
Converting 124% to a decimal (1.24) and dividing the final amount by this multiplier isolates the original pre-tax cost.

Key Concept

Calculating an original base price by dividing the final total by a growth factor multiplier (1 + combined percentage rate).
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Topics

Taxes and Tips

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