# Find the percent of the price

## Homework Statement

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?

## Homework 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!

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

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?

## Homework 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.

For 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!
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 ?

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 ?
0.09?

SammyS
Staff Emeritus
Homework Helper
Gold Member
0.09?
0.09?
No.

How did you calculate that ?

No.

How did you calculate that ?
1 -1.09/1=0.09

No.

How did you calculate that ?

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
1 -1.09/1=0.09
They would have paid 1.09, not 1.00.

Also, they pay 0.09 less

SammyS
Staff Emeritus
Homework Helper
Gold Member
I think I get it, 1 = 1.09(1+p), p = 0.08257
Yes.

That's it !

What is that as a percentage ?

Yes.

That's it !
For b, Lucy will rise the price by 0.08257?

SammyS
Staff Emeritus
Homework Helper
Gold Member
For b, Lucy will rise the price by 0.08257?
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 ? 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 ?
yes

SammyS
Staff Emeritus