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Math Help - Simultaneous Equation Problem...

  1. #1
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    Smile Simultaneous Equation Problem...

    Jane wants to prepare a special diet for her pets. She requires a food mixture that contains, among other things, 29 ounces of protein and 6 ounces of fat. Food mixes are available with the compositions shown in the table. How many ounces of each mix should she use to prepare the diet mix?

    In Mix A, there are 20% of protein and 2% of fat.
    In Mix B, there are 10% of protein and 6% of fat.

    I have no idea how to solve it but I know the answer is 114 ounces of Mix A and 62 ounces of Mix B. Thx.
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  2. #2
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    You have

    \frac{2}{10}x_A + \frac{1}{10}x_B = 29
    \frac{2}{100}x_A + \frac{6}{100}x_B = 6

    Solve the first equation for x_A and you get
    145 - \frac{1}{2}x_B
    Replace x_A in the second equation with that solution and solve for x_B, which should give you x_B = 62.
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  3. #3
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    Quote Originally Posted by clarebear14 View Post
    Jane wants to prepare a special diet for her pets. She requires a food mixture that contains, among other things, 29 ounces of protein and 6 ounces of fat. Food mixes are available with the compositions shown in the table. How many ounces of each mix should she use to prepare the diet mix?

    In Mix A, there are 20% of protein and 2% of fat.
    In Mix B, there are 10% of protein and 6% of fat.

    I have no idea how to solve it but I know the answer is 114 ounces of Mix A and 62 ounces of Mix B. Thx.
    let x = oz of mix A
    y = oz of mix B

    .2x + .1y = 29

    .02x + .06y = 6

    ------------------
    multiply the first equation by 10, the second by 100

    2x + y = 290

    2x + 6y = 600

    use elimination ...

    5y = 310

    y = 62

    and the value for x will follow.
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by clarebear14 View Post
    Jane wants to prepare a special diet for her pets. She requires a food mixture that contains, among other things, 29 ounces of protein and 6 ounces of fat. Food mixes are available with the compositions shown in the table. How many ounces of each mix should she use to prepare the diet mix?

    In Mix A, there are 20% of protein and 2% of fat.
    In Mix B, there are 10% of protein and 6% of fat.

    I have no idea how to solve it but I know the answer is 114 ounces of Mix A and 62 ounces of Mix B. Thx.
    Let the number of ounces of Mix A be x.

    Let the number of ounces of Mix B be y.

    \frac{20}{100}x+\frac{10}{100}y=29

    \frac{2}{100}x+\frac{6}{100}y=6

    Solving these 2 equations, we get x=114 and y=62.
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