Which systems of equations could be used to determine how much should be mixed to get 2 liters of the 40% solution?

Question

He only has a 25% solution and a 75% solution available. He wants to make a 40% solution of a certain solvent.

Answers:

A.) x+y=2                             B.) x+y=2

    .25x+.75y=.40                    .25x+.75y=2

 

 

C.) x+y=.40                          D.) x+y=2

     .25x+.75y=.40                     .25x+.75y=.80

 

Answer 1

The correct answer is D. 

The first equation must sum to the total amount of each solution when combined must be 2 liters. 

The 2nd equation is to calculate the amount of solute in the solution. so you take the percentage of each times the amount of each and then the .8 is (.4)(2). 

Answer 2

Let x = amount of 25% solution

     y = amount of 75% solution

     2 = amount of 40% mixture

 

Solvent content of 25% solution = 25% of x = 0.25x

Solvent content of 75% solution = 75% of y = 0.75y

Solvent content of 40% solution = 40% of 2 = 0.40(2) = 0.80

 

Amount of solution:   x + y = 2

Amount of solvent:  0.25x + 0.75y = 0.80

 

Answer:  D)