A pharmacist mixes a 40% acid solution and a 25% acid solution to get 115 Liters of a 33% solution. How much of each is mixed?

Question

Hello guys, I really need help with this question, Thanks in advanced. 

Answer 1

James:

 

 

Let x= number of liters of 40% acid solution and y= number of liters of 25% acid solution

 

Write two equations: the first based on the total number of liters of the three solutions

 

The second based on the amount of acid in each solution

 

We know that x + y = 115

 

The amount of acid in the 40%solution is .4x

 

The amount of acid in the 25% solution is .25y

 

The amount of acid when the two solutions are combined is 115(.33)

 

So the second equation is .4x + .25y = 115(.33)

 

Your two equations are: x + y = 115

                   and         .4x + .25y = 115(.33) becomes .4x + .25y = 37.95

 

Multiply the second equation by -4

 

So      x + y = 115  and

 

     (-4)(.4x) + (-4)(.25y) = (-4)(37.95)

 

         x + y = 115

 

      -1.6x -y = -151.80

 

Adding together:  -.6x = -36.80

 

Multiply by -100: 60x = 3680

 

Divide by 60 so x = 61.33

 

If x + y = 115  then 61.33 + y = 115  so y = 115 - 61.33 or 53.67

 

 

Denny Rose

Galion, OH