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Find the percent of the price

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  1. Oct 1, 2015 #1
    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. jcsd
  3. Oct 1, 2015 #2

    SammyS

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    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 ?
     
  4. Oct 1, 2015 #3
    0.09?
     
  5. Oct 1, 2015 #4

    SammyS

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    No.

    How did you calculate that ?
     
  6. Oct 1, 2015 #5
    1 -1.09/1=0.09
     
  7. Oct 1, 2015 #6
    I think I get it, 1 = 1.09(1+p), p = 0.08257
     
  8. Oct 1, 2015 #7

    SammyS

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    They would have paid 1.09, not 1.00.

    Also, they pay 0.09 less
     
  9. Oct 1, 2015 #8

    SammyS

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    Yes.

    That's it !

    What is that as a percentage ?
     
  10. Oct 1, 2015 #9
    For b, Lucy will rise the price by 0.08257?
     
  11. Oct 1, 2015 #10

    SammyS

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    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 ?
     
  12. Oct 1, 2015 #11
    yes
     
  13. Oct 1, 2015 #12

    SammyS

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    So how do you propose to fix that ?
     
  14. Oct 1, 2015 #13
    108.257=100(1+0.09)(1+p),p=0.0068, seems not right for me
     
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