Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs. Huang can use them. To apply herbicide to a large field she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution. How much of the 67% solution must she use? A. 18 L B. 34 L C. 35 L D. 23 L

To solve this problem, let us first assign variables. Let us say that:

x = volume of 67% herbicide solution

y = volume of 46% herbicide solution

The total volume should be 42 liters therefore:

x + y = 42

x = 42 - y - - > 1

The component mass balance on the pure herbicide would be:

0.67 x + 0.46 y = 0.55 (42) - - > 2

Substituting equation 1 to 2:

0.67 (42 - y) + 0.46 y = 23.1

28.14 - 0.67 y + 0.46 y = 23.1

- 0.21 y = - 5.04

y = 24 L

Calculating for x using equation 1:

x = 42 - 24

x = 18 L

Therefore we only need 18 L of the 67% herbicide solution.

Answer:

A. 18 L