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 18 l 34 l 35 l

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

d

step-by-step explanation:

d

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5