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Math Help - Matrices Word Problem/Application Questions

  1. #1
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    Matrices Word Problem/Application Questions

    First off, hello, hope you are having a good weekend.

    So for this question I am suppose to solve for it using a 3 x 4 matrix, so using the information below I would need 3 correct equations (AX + BY +CZ = _), which is my biggest problem.

    A farmer needs 500 kg of fertilizer that is 50% nitrogen, 15% phosphorus, and 35% potassium. Three different brands are available. Their compositions are shown below. How many kilograms of each brand should he use?

    Brand X: 40% nitrogen, 20% phosphorus, 40% potassium
    Brand Y: 50% nitrogen, 20% phosphorus, 30% potassium
    Brand Z: 60% nitrogen, 40% potassium

    Any help is appreciated
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  2. #2
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    Re: Matrices Word Problem/Application Questions

    Quote Originally Posted by ADRossi View Post
    First off, hello, hope you are having a good weekend.

    So for this question I am suppose to solve for it using a 3 x 4 matrix, so using the information below I would need 3 correct equations (AX + BY +CZ = _), which is my biggest problem.

    A farmer needs 500 kg of fertilizer that is 50% nitrogen, 15% phosphorus, and 35% potassium. Three different brands are available. Their compositions are shown below. How many kilograms of each brand should he use?

    Brand X: 40% nitrogen, 20% phosphorus, 40% potassium
    Brand Y: 50% nitrogen, 20% phosphorus, 30% potassium
    Brand Z: 60% nitrogen, 40% potassium

    Any help is appreciated
    let x = amount of brand X fertilizer in kg

    let y = amount of brand Y fertilizer in kg

    let z = amount of brand Z fertilizer in kg

    x + y + z = 500

    % nitrogen equation ...

    .4x + .5y + .6z = 250

    % phosphorus equation ...

    .2x + .2y = 75

    % potassium equation ...

    .4x + .3y + .4z = 175
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