# 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

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

18 L

Step-by-step explanation:

Let x L = the volume of 67 % herbicide Then

(42 - x) L = the volume of 46 % herbicide

We can calculate the mass of herbicide in each solution.

mass = volume × concentration

m = cV

For the three solutions, we can write

m₁ + m₂ = m₃

c₁V₁ + c₂ V₂ = c₃V₃

67 % × x L + 46 % × (42 - x) L = 55 % × 42 L

67x + 46(42 - x) = 2310

Distribute the 46

67x + 1932 - 46x = 2310

Combine like terms

21x + 1932 = 2310

Subtract 1932 from each side

21x = 378

Divide each side by 21

x = 18 L

Mrs. Huang must mix 18 L of 67 % herbicide with 24 L of 46 % herbicide to get 42 L of 55 % solution

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.

A. 18 L