# Thread: Matrices Word Problem/Application Questions

1. ## 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

2. ## Re: 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
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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