Animals in an experiment are to be kept under a strict diet. Each animal should receive 34 grams of protein and 5 grams of fat. The laboratory technician is able to purchase two food mixes: Mix A has 10% protein and 5% fat; mix B has 40% protein and 4% fat. How many grams of each mix should be used to obtain the right diet for one animal?

mix A = 40 gram

Mix B = 75 gram

Step-by-step explanation:

Each animal should receive 34 grams of protein and 5 grams of fat.

Food A ( x gram)

Protein = 0.1x

Fat = 0.05x

Food B ( y gram)

Protein = 0.4y

Fat = 0.04y

The grams of each mix should be used to obtain the right diet for one animal

Protein needed = 0.1x + 0.4y = 34

0.1x + 0.4y = 34 (1)

Fat needed = 0.05y + 0.04y = 5

0.05x + 0.04y = 5 (2)

Solve equation (1) and (2) simultaneously

x + 4y = 340

5x + 4y = 500

( note: I multiply (1) by 10 and equation (2) by 100)

- 4x = - 160

X = 40 gram

Substitute x in equation 1

4y = 300

Y = 75 gram

Therefore mix A = 40 gram

Mix B = 75 gram

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