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Math Help - systems of linear equations

  1. #1
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    systems of linear equations

    1. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?




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  2. #2
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    Quote Originally Posted by Patience View Post
    1. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?




    2.
    Hello, Patience,

    let x be the amount of the cheaper coffee
    let y be the amount of the more expensive coffee

    then you get a system of simultanous equations:

    A: x + y = 100
    B: 9x + 12y = 11.25 * 100

    I don't know which method you use to solve this system but you should get the results:
    x = 25 and y = 75

    EB
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    x + y = 100....(i)
    9x + 12y = 1125....(ii)

    (i) --> x = 100-y

    (ii) --> 9(100-y) + 12y = 1125

    900 - 9y + 12y = 1125
    3y = 225
    y = 75

    (i) --> x = 100-75

    x =25
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