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How to solve simple Percentages problem?

  1. May 29, 2010 #1
    1. The problem statement, all variables and given/known data
    Q1. A shop's normal price for a camera is $175. If prices are temporarily reduced by 7.5%, what is the new price of the camera?

    Q2. In a sale, a shop reduces its prices by the amount of the VAT on each item. If VAT is 17.5%, what is the percentage price reduction? (Hint: The answer is not 17.5%)


    2. The attempt at a solution
    Q1. 7.5+100 /100 = 1.075
    $175 /1.075 = $162.79

    Q2.
    I assume item x = $100
    VAT = 17.5% of $100 = $17.5 on that item
    To find price before VAT = 100+17.5 /100= 1.175
    100 /1.175= $85.11
    100-85.11 = $14.89

    I don't know how to find the "percentage price reduction". The reduction in absolute terms seems to be $14.89 on a $100 item. And I know Q1 is wrong too. I don't know how to solve questions that are worded in english like this.

    Please help.
     
  2. jcsd
  3. May 29, 2010 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi vitaminZ ! Welcome to PF! :smile:
    In English, "reduced by 7.5%" means that the new price is (100 minus 7.5)/100, = 0.925.

    So to reduce the price by 7.5%, you multiply it by 0.925 (check, and you'll see that this is not exactly the same as dividing by 1.075 :wink:)

    (Always multiply, never divide!)
    If the basic price is $100, then the VAT is $17.5, so the total price is $117.5.

    "percentage price reduction" means the fraction (as a percentage) by which you must reduce the total price to get the reduced price (ie, the basic price, without the VAT) …

    ie by what fraction must you reduce 117.5 to get 100? :smile:

    So … your answer is very nearly complete, except …

    i] you should keep "x" as "x", not make it 100

    ii] your fractions are dollars/dollars, which is just a number (ie, don't write "$14.89", write "14.89%", or "0.1489")

    iii] it would be quicker to use the difference ($17.5) to make the fraction :wink:
     
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