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?

18L

Explanation:

Solving this question would be easier by assigning variables.

so, let x = amount of 67% needed solution

Let y = amount of 42% needed solution.

From the question, we know that

x + y = 42 thus,

y = 42 - x

we also know that the pure herbicide in the 67% solution plus the herbicide I'm the 46% solution must be equal to the amount of pure herbicide in the final solution. Thus mathematically, we have

0.67x + 0.46y = 0.55*42

0.67x + 0.46y = 23.1

Remember, y = 42 - x, substituting this value, we have

0.67x + 0.46(42-x) = 23.1

0.67x + 19.32 - 0.46x = 23.1

0.21x = 23.1 - 19.32

0.21x = 3.78

x = 18

.therefore the amount of 67% solution needed is 18L