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Math Help - Percents of Solution

  1. #1
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    Percents of Solution

    A printer has ink that is 8% cobalt blue color and ink that is 22% cobalt blue color. How many ounce of each ink are needed to make 64 ounces of ink that is 15% cobalt blue color?


    I am getting .08x+14.08-22x=9.6
    -14.08 -14.08
    -21.92x=-4.48
    divide -21.92 x= A Nasty Decimal that doesnt make make it right......
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  2. #2
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    Re: Percents of Solution

    Quote Originally Posted by maes0732 View Post
    A printer has ink that is 8% cobalt blue color and ink that is 22% cobalt blue color. How many ounce of each ink are needed to make 64 ounces of ink that is 15% cobalt blue color?


    I am getting .08x+14.08-22x=9.6
    -14.08 -14.08
    -21.92x=-4.48
    divide -21.92 x= A Nasty Decimal that doesnt make make it right......
    1. Let x denote the amount of the 8%-ink and y the amount of the 22%-ink. Convert the percentasges into decimal fractions. Then you know:

    \left|\begin{array}{rcl}x+y&=&64 \\ 0.08 x + 0.22 y &=& 0.15 \cdot 64 = 9.6 \end{array} \right.

    2. Solve for x and y. I've got x = 32 and y = 32.
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  3. #3
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    Re: Percents of Solution

    Ok i will try that out. The way our teacher explained the problems was different. He made us put them in like a table and one ink is obviously X and then the other ink is the 64 ounces to start with so 64-X, but i will give that method a try on a few.
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  4. #4
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    Re: Percents of Solution

    Quote Originally Posted by maes0732 View Post
    Ok i will try that out. The way our teacher explained the problems was different. He made us put them in like a table and one ink is obviously X and then the other ink is the 64 ounces to start with so 64-X, but i will give that method a try on a few.
    It's better to understand the problem/solution than to imitate the teacher...
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  5. #5
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    Re: Percents of Solution

    You have the best solution for the problem by earboth. But the way your want to do it as below (some times lower grades teacher don't teach system of linear equations)

    Consider X ounces of 8% cobalt, (64 - x) ounces of 22% cobalt are mixed to get 64 ounces of 15% cobalt

    Let's write an equation using the above values

    8x + 22(64 - x) = 15*64

    8x + 1408 - 22x = 960

    -14x = 960 - 1408

    -14x = -448
    x = 32
    So, 32 ounces of 8% cobalt, (64 - 32)=32 ounces of 22% cobalt ink is needed.
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  6. #6
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    Re: Percents of Solution

    Code:
       a  @ x
       b  @ y
    =========
    (a+b) @ z
    z = (ax + by) / (a + b)
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