River's chemistry class is doing an experiment in which the students create a 30% hydrochloric acid mixture by mixing a certain amount of 25% solution with a different amount of 50% solution. The amount of 25% solution used is 20 liters less than 5 times the amount of 50% solution used. How much of the 25% solution and the 50% solution are needed in all

20 liters of 50% solution and 80 liters of 25% solution

Explanation:

Let x litres be the amount of 50% solution to be used.

Since the amount of 25% solution used is 20 liters less than 5 times the amount of 50% solution used, then the 25% solution would be (5x -20) litres.

Therefore, 50x + 25(5x-20) = 30(x + 5x-20)

50x + 125x - 500 = 30x + 150x - 6 00

175x - 500 = 180x - 600

Collecting like terms

180x - 175x = 600 - 500

5x = 100

x = 20

Therefore, volume of 50% solution needed = 20 litres

Volume of 25% solution needed = (5 * 20) - 20 = 80 litres

20 liters of 50% solution and 80 liters of 25% solution