A botanist can purchase plant food of 4 different types I II

A botanist can purchase plant food of 4 different types, I, II, III, and IV. Each food comes in the same size bag and the following table summarizes the number of grams of each of three materials that each bag contains.

                                                Foods

I

II

III

IV

Nutrient A

5

5

10

5

Nutrient B

10

5

30

10

Nutrient C

5

15

10

25

The botanist wants to use a food that has these nutrients in a different proportion and determines that he will need a total of 10,000 g of A, 20,000 of B, and 20,000 of C. Find the number of bags of each type of food that should be ordered.

Solution

I

II

III

IV

Nutrient A

5

5

10

5

Nutrient B

10

5

30

10

Nutrient C

5

15

10

25