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Math Help - Find the Cost

  1. #1
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    Smile Find the Cost

    A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars,
    x > 100, at 8 a.m., what, in terms of x, is the cost of Hakeemís purchase?

    (1) 0.20x - 15 (3) 0.85x - 20
    (2) 0.20x -3 (4) 0.80x - 12...This is the answer.


    MY Work:

    I understand the situation in the question. The correct answer is highlighted in red. I selected choice (1) given the fact that Hakeem purchased an item over $100 and that the store offers a discount of $15 and an additional discount of 20%.

    It made sense to easily come up with 0.20x - 15. In fact, I also decided to let C = cost and then went on to develop the equation C = 0.20x - 15.

    Why is choice (4) correct and my answer incorrect?

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  2. #2
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    Quote Originally Posted by magentarita View Post
    A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars,
    x > 100, at 8 a.m., what, in terms of x, is the cost of Hakeem’s purchase?

    (1) 0.20x - 15 (3) 0.85x - 20
    (2) 0.20x -3 (4) 0.80x - 12...This is the answer.


    MY Work:

    I understand the situation in the question. The correct answer is highlighted in red. I selected choice (1) given the fact that Hakeem purchased an item over $100 and that the store offers a discount of $15 and an additional discount of 20%.

    It made sense to easily come up with 0.20x - 15. In fact, I also decided to let C = cost and then went on to develop the equation C = 0.20x - 15.

    Why is choice (4) correct and my answer incorrect?
    You've subtracted the 20% discount before the $15 deduction. The 20% discounted is subtracted after the $15 deduction.

    (x - 15) - 20% of (x - 15) = x - 15 - \frac{1}{5} \, (x - 15) = x - 15 - \frac{x}{5} + 3 = \frac{4}{5} x - 12.
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  3. #3
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    I see...

    Quote Originally Posted by mr fantastic View Post
    You've subtracted the 20% discount before the $15 deduction. The 20% discounted is subtracted after the $15 deduction.

    (x - 15) - 20% of (x - 15) = x - 15 - \frac{1}{5} \, (x - 15) = x - 15 - \frac{x}{5} + 3 = \frac{4}{5} x - 12.
    I did not keep the order.

    Got it.
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