Question

An herbalist is mixing a 9-kilogram batch of a medicinal blend. The blend, which costs $25.05 per kilogram to make, is made up of ground ginseng at $33.85 per kilogram and golden chia at $16.25 per kilogram. How many kilograms of each should be used to make the 9-kilogram batch?

Write your answers as whole numbers or as decimals rounded to the nearest tenth.

Answer 1

To make a 9-kilogram batch of a medicinal blend, approximately 3.81 kilograms of ground ginseng and 5.19 kilograms of golden chia should be used.

Step-by-step explanation:

To find how many kilograms of each blend should be used to make a 9-kilogram batch, we can set up a system of equations.

Let x represent the number of kilograms of ground ginseng and y represent the number of kilograms of golden chia.

The cost of the blend is given by the equation 33.85x + 16.25y = 25.05(9).

The total weight of the blend is given by the equation x + y = 9.

We can solve this system of equations to find x and y. Multiplying the second equation by 33.85 and subtracting it from the first equation, we get:

33.85x + 16.25y - 33.85x - 33.85y = 25.05(9) - 33.85(9)

-17.6y = -91.35

y = 5.19

Substituting the value of y back into the second equation, we get:

x + 5.19 = 9

x = 9 - 5.19

x = 3.81

Therefore, approximately 3.81 kilograms of ground ginseng and 5.19 kilograms of golden chia should be used to make a 9-kilogram batch.