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? 23 l 35 l 34 l 18 l

18 L

Step-by-step explanation:

Given :  she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution.

To Find: How much of the 67% solution must she use?

Let x = amount of 67% solution needed

Then 42-x=amount of 46% solution needed

Now we know that the pure herbicide in the 67% solution

So, pure herbicide = (0.67x)

The amount of pure herbicide in the 46% solution (0.46(42-x))

Now 42 liters of a 55% solution = (0.46(42-x))

So,

Amount of 67% solution + Amount of 46% solution  = 42 liters of a 55% solution

⇒0.67x+0.46(42-x)=0.55*42  

⇒0.67x+19.32-0.46x=23.1

⇒0.21x=3.78

⇒

⇒x = 18 liters

Hence she use 18 liters of the 67% solution