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Thread: Basic Algebra Word Problem Practice

  1. #1

    Question Basic Algebra Word Problem Practice

    Hello all...I have an upcoming ACT test, and I'm reviewing all of the necessary math skills. However, there is a very basic algebra practice problem, and I don't understand the solution provided in the work book. Here's the problem itself:

    A grocer has two kinds of candy, one selling for $1.20 a dekagram (a tenth of a kilogram) and the other selling $1.80 a dekagram. He wants to sell a mixture of the two for $1.60 a dekagram. How much of each should he use to make 60 dekagrams of the mixture?

    And here's the provided solution:

    Start by assigning the value of the necessary number of dekagrams, n, of the cheaper candy at 120n cents. The number of dekagrams of the more expensive candy must be 60 n. Therefore, the value of the more expensive candy in cents is 180(60 n). The total value of the mixture in cents is to be 160(60).

    120n + 180(60 n) = 160(60)

    I do not understand where (60 n) comes from--? What does that represent, and how did they arrive at it? Any help would be appreciated.
    Last edited by studyrose; 02-13-2012 at 05:18 PM.

  2. #2
    Senior Member
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    Quote Originally Posted by studyrose View Post
    I am 30 years old, and I have an upcoming ACT test, so I'm reviewing all of the necessary math skills. However, I have a very basic algebra practice problem, and I don't understand the solution provided in the work book. Here's the problem itself:

    A grocer has two kinds of candy, one selling for $1.20 a dekagram (a tenth of a kilogram) and the other selling $1.80 a dekagram. He wants to sell a mixture of the two for $1.60 a dekagram. How much of each should he use to make 60 dekagrams of the mixture?

    And here's the provided solution:

    Start by assigning the value of the necessary number of dekagrams, n, of the cheaper candy at 120n cents. The number of dekagrams of the more expensive candy must be 60 n. Therefore, the value of the more expensive candy in cents is 180(60 n). The total value of the mixture in cents is to be 160(60).

    120n + 180(60 n) = 160(60)

    In the provided equation, I do not understad where (60 n) comes from--? What does that represent, and how did they arrive at it? Any help would be appreciated. Thank you in advance!
    The grocer wants to end up with a total of 60 dekagrams of the mixture.

    If he uses "n" dekagrams of cheaper candy, the REST of the 60 dekagrams, or (60 - n) dekagrams, must be the more expensive candy. Then, there will be a total of 60 dekagrams in the mixture: n + (60 - n) = 60.

    If the total of two things is 60, and ONE of the things is "n", the other must be 60 - n.

  3. #3

    Smile

    Okay, that actually makes sense. Wow, thank you so much for the quick response. I really couldn't get my mind around that--thanks again to you both, that really helps!
    Last edited by studyrose; 02-13-2012 at 05:35 PM.

  4. #4
    Elite Member
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    Code:
    ITEM  COST
      a  @ x
      b  @ y
    ========
    a+b  @ z
    z = (ax + by) / (a + b)
    I'm just an imagination of your figment !

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