Animals in an experiment are to be kept under a strict diet. Each animal should receive 18 grams of protein...

Question

Animals in an experiment are to be kept under a strict diet. Each animal should receive 18 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?
One animal's diet should consist of ______ grams of Mix A.

SnapAndSolve AI · Accepted Answer

Let x be the grams of Mix A and y be the grams of Mix B.

Protein equation: 0.10x + 0.40y = 18
Fat equation: 0.05x + 0.04y = 5

Solving these equations simultaneously:

Multiply the fat equation by 10 to eliminate decimals: 0.5x + 0.4y = 50
Now solve the system:
From the protein equation: 0.10x + 0.40y = 18
From the modified fat equation: 0.5x + 0.4y = 50
Subtract the protein equation from the modified fat equation:
(0.5x + 0.4y) - (0.10x + 0.40y) = 50 - 18
0.4x = 32
x = 80
Substitute x = 80 into the protein equation:
0.10(80) + 0.40y = 18
8 + 0.40y = 18
0.40y = 10
y = 25

Therefore, one animal's diet should consist of 80 grams of Mix A and 25 grams of Mix B.

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Animals in an experiment are to be kept under a strict diet. Each animal should receive 18 grams of protein...

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