# Matrices and equations

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Protein, carbohydrates, and fats can be obtained from three foods. Each ounce of food I contains 5 grams of protein, 10 grams of carbohydrates, and 40 grams of fat. Each ounce of Food II contains 10 grams of protein, 5 grams of carbohydrates, and 30 grams of fat. Each ounce of Food III contains 15 grams of protein, 15 grams of carbohydrates, and 80 grams of fat. How many ounces of each of the three foods are required to yield 300 grams of protein, 300 grams of carbohydrates, and 1500 grams of fat? (arrive at your conclusion, define variables, set up a system of equations, and solve it using matrix methods.)

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##### Solution Summary

This is a mixture problem to create food with the given nutritional requirements.

##### Solution Preview

If we assume that each ounce is approximately 30 grams, then the mixture must have 10 ounces of protein, 10 ounces of carbohydrates and 50 ounces of fat. We can then set up the following system:

=

where x is the amount of the first food, y ...

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