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    Bronze Lounger Maudibe's Avatar
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    Basic Math Problem?

    An instrument store gives a 10% discount to all students off the original cost of an instrument. During a “Back to school” sale, an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?

    Good luck,
    Maud

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    $400

    Do I have to show my work, teacher?

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    Or if one figures in 5% sales tax, $381 give or take a few pennies, but there are also a couple potential trick elements in the mix, like if the instrument was not purchased there or what original cost might actually mean.
    Last edited by F.U.N. downtown; 2013-07-19 at 10:51.

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    Silver Lounger mrjimphelps's Avatar
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    Not figuring in any tax, the original price was $345.76.

    Update -- should be $353.76.
    Last edited by mrjimphelps; 2013-07-19 at 11:10. Reason: recalculated

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    Silver Lounger mrjimphelps's Avatar
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    Quote Originally Posted by F.U.N. downtown View Post
    Or if one figures in 5% sales tax, $381 give or take a few pennies, but there are also a couple potential trick elements in the mix, like if the instrument was not purchased there or what original cost might actually mean.
    My guess is that "original cost" means what the customer would have paid had there been no discounts.

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    Super Moderator BATcher's Avatar
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    It's easy maths: $306 / 0.9 / 0.85 = $400. But surely it would, in reality, be priced at $399.99?!
    BATcher

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    Quote Originally Posted by mrjimphelps View Post
    My guess is that "original cost" means what the customer would have paid had there been no discounts.
    That's one interpretation, also might be what the instrument store paid for it or what the manufacturer cost to make was. I'm production-based so the latter is what original cost means to me, before the middlemen and retailer add to the original cost.

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    Silver Lounger mrjimphelps's Avatar
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    Quote Originally Posted by BATcher View Post
    It's easy maths: $306 / 0.9 / 0.85 = $400. But surely it would, in reality, be priced at $399.99?!
    400 minus 10% (40) would be 360. Then 15% off of that (54) would be 360 minus 54 or 306.

    I have a minor in math, but this problem tripped me up!

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    Ya, and just divide by the sales tax amount prior to the two discounts for extra credit.
    306/1.05/.85/.9=$380.95

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    Super Moderator BATcher's Avatar
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    In the UK, although we have an iniquitous rate - 20% usually - of "Value Added Tax" (VAT), it is always included in the price for consumer purchases, so "the price you see is the price you pay" (haggling excepted).

    For electronic goods and software, there seems to be a special "$1 translates to £1" conversion rate, which is why the UK is often referred to by non-native computer and software manufacturers as "Treasure Island". I have no idea whether this conversion rate also applies to the cost of flutes...
    BATcher

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    Bronze Lounger Maudibe's Avatar
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    This was an actual question given in a math class for education of immigrants to achieve a GED. The answer choices offered were:
    A. $325.00
    B. $375.00
    C. $400.00
    D. $408.00
    E. $425.00

    The most selected and also incorrect answer was $408.00 achieved by adding the 2 discounts (25%), calculating a discount of $102.00, then subtracting it from $408.00 which was a final price of $306.00.

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    A 10% discount OFF the original price leaves 90% ON the original price.
    If X is the original price, the first resulting price is 0.9X.

    Then, if 15% is OFF this discounted price, that leaves 85% ON the price.

    So, 0.85 x 0.9 x X = 306 (purchase).

    Then, X = 306/0.765 = $400 as the original price.

    Check it: $400 with a 10% discount = $360 ($40 off).
    Then, 360 with a 15% discount = $54 off the $360.
    So, 360 - 54 = $306.
    Last edited by kweaver; 2013-07-20 at 13:19.

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    2 Star Lounger
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    Quote Originally Posted by BATcher View Post
    For electronic goods and software, there seems to be a special "$1 translates to £1" conversion rate...
    When I was in London some years ago, the same seemed to apply to books, especially paperbacks. Whatever number the US publisher printed on the book, that was the number of pounds charged. The currency exchange rate at the time was about 1.75 to 1, plus the fee at the exchange kiosk.

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