Question 4 (3 marks) I wish to prepare a meal which contains 31 grams of protein

Question

Question 4 (3 marks) I wish to prepare a meal which contains 31 grams of proteins, 19 grams of fats and 61 grams of carbohydrates. Three ingredients are available with the nutritional content per 100 grams given by the following table Write a matrix equation to enable me to determine what quantity of each ingredient I should use, stating clearly what the unknown variables represent. (Do not solve the matrix equation: the purpose of the question is to see if vou can translate the description of a problem into mathematics. You have already demonstrated in Question 4 whether you know how to solve a matrix equation Proteins Fats Carbohydrates 10 75 15 Ingredient 1 Ingredient 2 Ingredient 3 32 12

Explanation / Answer

Let x grams of ingredient 1, y grams of ingredient 2 and z grams of ingredient 3 be used to prepare a meal containing 31 grams of protein, 19 grams of fats and 61 grams of carbohydrates. Then we have:

0.15x+0y+0.32z = 31…(1)

0.09x+0.05y+0.12z = 19…(2) and

0.10x+0.75y+0.05z = 61…(3).

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