The table shows the amount (in g) of protein, carbohydrate, and fat supplied by

Question

The table shows the amount (in g) of protein, carbohydrate, and fat supplied by one unit (100 g) of three different foods.
FOOD X (PROTEIN, CARBO, FAT )
FOOD 1 (15,45,6)
FOOD 2 (35,30,4)
FOOD 3 (25,50,1)

Betty would like to prepare a meal using some combination of these three foods. She would like the meal to contain 15 g of protein, 25 g of carbohydrate, and 3 g of fat. How many units of each food should she use so that the meal will contain the desired amounts of protein, carbohydrate, and fat? Round to 3 decimal places.

Explanation / Answer

15x+35y+25z=15 45x+30y+50z=25 6x+4y+1z=3 (15 35 25 15) = (1 0 0 0.326) x=0.326 (45 30 50 25) (0 1 0 0.247) y=0.247 ( 6 4 1 3 ) (0 0 1 0.059) z=0.059 food 1 = 0.326 food 2 = 0.247 food 3 = 0.059

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