Jenna needs 100 liters of 15% alcohol solution. If she has a 12% alcohol solution and a 20% alcohol solution available, how much of each should she mix to get the desired solution?

67.5 litres of 12% alcohol and 37.5 litres of 20% alcohol

Step-by-step explanation:

To solve this question, the principle of going by average is needed, that is the average of both initial Alcohol solution is what is needed to get the exact alcohol solution being demanded in the question.

Let the litres of 12% to be mixed be denoted as xlitres

This means the liters of 20% to be mixed will be denoted as (100 - x) litres

Hence to get the exact 100 litres of 15%, we go by the Formula

[12 * x] + [20 * (100 - x) ] = 100 * 15.

12x + 2000 - 20x = 1500

-8x + 2000 = 1500

2000 - 1500 = 8x

500 = 8x

x = 500/x

x = 62.5 Litres

100 - 62.5 = 37.5 Litres.

This means the mixture of 62.5 lites of 12% of alcohol and 37.5 litres Of 20% alcohol will give exactly 100litres of 15% alcohol.