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?

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

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