A solution of 67% pesticide is to be mixed with a solution of 57% pesticide to form 30 liters of a 59% solution. How much of the 67% solution must she use?

Question

Tell what x= and y= 

 

Give both equations you deduce from the story problem with a bracket.

 

You may use substitution, elimination, or graphing for the solution to the system. Show all work for the method you choose.

 

Label the solutions. tell what your answers mean by putting labels on the answers.

Answer 1

Let x = number of liters of 67% solution

      y = number of liters of 57% solution

 

Then, x + y = 30

   and 0.67x + 0.57y = 0.59(30)

 

Multiply the first equation by -0.67:

 

-0.67x - 0.67y = -20.1

 0.67x + 0.57y = 17.7

 

Add the equations to get: -0.10y = -2.4

 

                                                      y =  24   and x = 30 - y = 6

 

Use 6 liters of 67% solution and 24 liters of 57% solution to obtain 30 liters of 59% solution.