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Math Help - Word problem - with confusing phrasing

  1. #1
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    Word problem - with confusing phrasing

    Last week, Dolly bought x kg of grade B coffee powder for $12. If she bought grade A coffee powder instead, she would get 200 g less for $12. This week, the price of coffee powder for both grades increased by $5.00 per kg. If Dolly buys grade A coffee powder instead of grade B coffee powder, she will get 120 g less for $12.

    Find how much grade B coffee powder Dolly bought last week.

    I am thinking on the lines of quantity for week 2 x unit price for week 2 = 12 will yield a quadratic equation to solve.

    But, I am confused with the second half of the problem. Does the 120 g less mean that she will get grade A coffee less that grade A for previous week or less that grade B this week?

    Thanks for your help.

    Edit: Sorry forgot the question part!
    Last edited by mathguy80; March 12th 2011 at 12:51 AM. Reason: incomplete question
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  2. #2
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    Quote Originally Posted by mathguy80 View Post
    Last week, Dolly bought x kg of grade B coffee powder for $12. If she bought grade A coffee powder instead, she would get 200 g less for $12. This week, the price of coffee powder for both grades increased by $5.00 per kg. If Dolly buys grade A coffee powder instead of grade B coffee powder, she will get 120 g less for $12.

    I am thinking on the lines of quantity for week 2 x unit price for week 2 = 12 will yield a quadratic equation to solve.

    But, I am confused with the second half of the problem. Does the 120 g less mean that she will get grade A coffee less that grade A for previous week or less that grade B this week?

    Thanks for your help.
    1. x := amount of grade A coffee
    a:= old price per kg grade A coffee
    a + 5 := new price per kg grade A coffee

    2. According to the text you know:

    (x-0.2) \cdot a = 12

    (x-0.2-0.12) \cdot (a+5)=12

    3. Determine x from the 1st equation and replace the variable x in 2nd equation by this term. Solve for a.
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    Thanks @earboth for your help.

    I forgot the most important part of the question, Sorry! The question is, Find how much grade B coffee powder Dolly bought last week.

    I am a little confused about your use of x. The question has the variable x with x Kg of grade B coffee powder. Is this a different variable x? I solved the equation assuming a different x. And got x = 40 kg, so corresponding grade B would be 40.2 Kg. This doesn't fit the answer at the back, which is x = 0.8 Kg. Did i solve it right?
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  4. #4
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    Quote Originally Posted by mathguy80 View Post
    Thanks @earboth for your help.

    I forgot the most important part of the question, Sorry! The question is, Find how much grade B coffee powder Dolly bought last week.

    I am a little confused about your use of x. The question has the variable x with x Kg of grade B coffee powder. Is this a different variable x? I solved the equation assuming a different x. And got x = 40 kg, so corresponding grade B would be 40.2 Kg. This doesn't fit the answer at the back, which is x = 0.8 Kg. Did i solve it right?
    1. You are absolutely right: The x denotes the amount of grade B coffee.

    2. From the 1st equation (of post #2) you'll get: x = \dfrac{12}a + 0.2

    3. Replace the variable x by this term:

    \left(\dfrac{12}a + 0.2-0.2-0.12\right)(a+5)=12~\implies~-0.12a^2-0.6a+60=0

    4. Solve for a. I've got a = $20 per kg of B-coffee(The negative solution isn't very plausible here!)

    5. Then x = 0.6 + 0.2 = 0.8. So Dolly bought 0.8 kg B-coffee and she would have got 0.6 kg A-coffee for the same price.
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  5. #5
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    Got it! I also had a mistake in my quadratic solution. After fixing it got a = -25 (rejected) and a = 20.
    Then got x = 0.8.

    Excellent. Thanks for clearing this up. I went from to in a few hours. It was very helpful!
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