# Find the percent of the price

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1. Oct 1, 2015

### HaLAA

1. The problem statement, all variables and given/known data
a. 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?

b. 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?

2. Relevant equations

new price = old price(1+percentage)
new price = old price(1-percentage)

3. The attempt at a solution

let the price be 100

a. 100(1+9%)(1-9%)=99.19, 1-99.19/100=0.0082, the customer saves 0.82%

b. for this question, I don't quite understand this question.

Fot a, it seems that I did it completely wrong because b says Lucy doesn't want to pay the tax.

Can someone give me a hit or suggestion to do these two questions? Thanks!

2. Oct 1, 2015

### SammyS

Staff Emeritus
For (a)

For a $1.00 item, the customer formerly paid$1.09. After Lucy covers the tax, they only pay $1.00. What percent are they saving compared to the$1.09 they used to pay ?

3. Oct 1, 2015

0.09?

4. Oct 1, 2015

### SammyS

Staff Emeritus
No.

How did you calculate that ?

5. Oct 1, 2015

### HaLAA

1 -1.09/1=0.09

6. Oct 1, 2015

### HaLAA

I think I get it, 1 = 1.09(1+p), p = 0.08257

7. Oct 1, 2015

### SammyS

Staff Emeritus
They would have paid 1.09, not 1.00.

Also, they pay 0.09 less

8. Oct 1, 2015

### SammyS

Staff Emeritus
Yes.

That's it !

What is that as a percentage ?

9. Oct 1, 2015

### HaLAA

For b, Lucy will rise the price by 0.08257?

10. Oct 1, 2015

### SammyS

Staff Emeritus
So, on $100 worth of product under the old price, you're saying that she will now charge (take in)$108.257 .

Caesar, or whomever Lucy pays taxes to, will then take 9% of that. Lucy will not realize the \$100 that would have formerly received. Right ?

11. Oct 1, 2015

### HaLAA

yes

12. Oct 1, 2015

### SammyS

Staff Emeritus
So how do you propose to fix that ?

13. Oct 1, 2015

### HaLAA

108.257=100(1+0.09)(1+p),p=0.0068, seems not right for me