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

< > according to newton's third law of motion, forces always act in equal but opposite pairs. another way of saying this is for every action, there is an equal but opposite reaction.< >