Bill Lutes's dog is on a strict diet. The dog is to receive, among other nutrients, 3232 grams of protein and 5.65.6 grams of carbohydrates. Bill has only two food mixes available of the following compositions. How many grams of each mix should be used to obtain the right diet for his dog?

Using a system of equations, the number of grams of each mix required to make the right diet would be ; Mix A and B are 80 and 40 grams respectively.

For protein :

0.3a + 0.2b = 32 (1)

0.06a + 0.02b = 5.6 - - - (2)

Multiply (1) by 1 and (2) by (5)

0.3a + 0.2b = 32 (3)

0.3a + 0.1b = 28 - - - - - (4)

Subtract (4) from (3)

0.1b = 4

b = 40

From (1) :

0.30a + (0.20)40 = 32

0.30a = 32 - 8

0.30a = 24

a = 80

Hence, the required grams of Mix A and B are 80 and 40 grams respectively.

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80g of A and 40g of B must be mixed.

Step-by-step explanation:

The mixes are:

Mix        Protein (%)      Carbohydrate (%)

Mix A           30                        6

Mix B           20                        2

The following equations can be formed using the provided data:

0.30A + 0.20B = 32...(i)

0.06A + 0.02B = 5.6...(ii)

Multiply (ii) by 5 and subtract the resultant equation from (i):

0.30A + 0.20B = 32

-0.30A - 0.10B = -28

0.10B = 4

B = 40

Substitute B in (i) and solve for A as follows:

0.30A + (0.20 × 40) = 32

0.30A = 32 - 8

0.30A = 24

A = 80

Thus, 80g of A and 40g of B must be mixed.

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