A chemical stockroom

Question

A chemical stockroom has a 20% alcohol solution and a 50% alcohol solution. How many deciliters of each should be used to obtain 90 deciliters of a 30% solution?

Answer 1

Let x = number of deciliters of 20% solution

Then, 90 - x = number of deciliters of 50% solution

 

Acid content of 20% solution + acid content of 50% solution = acid content of the mixture

 

So, 0.20x + 0.50(90 - x) = 0.30(90)

 

      0.20x + 45 - 0.50x = 27

 

                          -0.30x = -18

 

                                   x = 60 and 90 - x = 30

 

Use 60 deciliters of 20% solution and 30 deciliters of 50% solution to obtain 90 deciliters of 30% solution.