Anna enjoys dinner at a restaurant in Washington DC where the sales tax on meals is 5%. She leave a 20% tip on the price of her meal before the sales tax is added and the tax is calculated on the pre-tip amount. She spends a total of $65.50 for dinner. What is the cost of her dinner without tax or tip?

Question

Mathematics

Short Shorts

8 March, 21:11

Anna enjoys dinner at a restaurant in Washington DC where the sales tax on meals is 5%. She leave a 20% tip on the price of her meal before the sales tax is added and the tax is calculated on the pre-tip amount. She spends a total of $65.50 for dinner. What is the cost of her dinner without tax or tip?

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Answers (1)

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Pugsley · Answer 1

52.40

Step-by-step explanation:

Discussion

Suppose the meal starts out as x.

She pays 5% of x as a sales tax

So that brings the total up to 100% + 5% = 105%

Before paying, she pays 20% on x as her tip. The tax does not touch the tip.

So that brings the total up to 100% + 5% + 20% = 125% of this is based on x, the cost of the meal.

So 125% of x = 65.50 change the % to a fraction

125/100 * x = 65.50 Multiply both sides by 100/125

125/100 * 100/125x = 100/125 * 65.50

x = 100/125 * 65.50 Multiply by 100

x = 6550 / 125 Divide by 125

Check

Tax = 5% * 52.40 = 5/100 * 52.40 = 2.62

Tip = 20%*52.40 = 20/100 * 52.40=10.48

Meal = 52.40

Total 65.50 Just as it should