Question

Lucy's Lunch and Latte has found that customers are put off by the local tourism tax of 9% that is added to their bill. If Lucy decides to cover the tax herself, rather than adding it to the customer's bill, what percent will the customer see in savings?   Write your answer as a percent rounded to the nearest tenth. (Hint: the answer is not 9%.)

Lucy decides to quietly raise her prices before announcing that she will pay the 9% tax. What percent should she raise her prices so that she will still end with the same amount as when the customer paid the tax, rather than her? Write your answer as a percent rounded to the nearest tenth. (Hint: again the answer is not 9%.)

Answer 1

1.  Let the initial price be x

Tax = (9/100) * x = 0.09x

Price after tax = (x + 0.09x) = 1.09 x

a) Since Lucy decides to cover the tax herself, amount saved by customer = 0.09x

Percent saved by the customer = (0.09x/1.09x) * 100 = 8.26 %

b) Let the price be increased by p %

New price before tax = x + (p/100) *x = (1 + 0.01p)x

Tax = (9/100)(1 + 0.01p)x = 0.09x(1 + 0.01p)

Now Lucy announces to cover the tax herself,so amount earned by her = (1 + 0.01p)x - 0.09x(1 + 0.01p)

= 0.91x(1 + 0.01p)

Since, it is given that she ends up with the same amount as when the customer paid the tax, rather than her

Therefore,

0.91x(1 + 0.01p) = 1.09x

=> 0.91 (1 + 0.01p) = 1.09

=> 0.91 + 0.0091p = 1.09

=> 0.0091 p = 0.18

=> p = 19.78%

So the price should be increased by 19.78%