Question

Jotham needs 70 liters of a 50% alcohol solution. He has a 30% solution and an

80% solution available. How many liters of the 30% solution and how many liters
of the 80% solution should he mix to make the 50% solution?

Answer 1

To make a 50% alcohol solution, Jotham needs to mix the 30% solution and the 80% solution. For every x liters of the 30% solution, Jotham needs 2x/3 liters of the 80% solution to make the 50% solution.

Step-by-step explanation:

To make a 50% alcohol solution, Jotham needs to mix the 30% solution and the 80% solution. Let's say he needs x liters of the 30% solution and y liters of the 80% solution. The total volume of the final solution will be x + y liters. Now, let's set up the equation based on the alcohol content:

0.30x + 0.80y = 0.50(x + y)

Simplifying the equation:

0.30x + 0.80y = 0.50x + 0.50y

0.30x - 0.50x = 0.50y - 0.80y

0.20x = 0.30y

0.2x = 0.3y

Simplifying further:

2x = 3y

Dividing both sides by 3:

2x/3 = y

So, for every x liters of the 30% solution, Jotham needs 2x/3 liters of the 80% solution to make the 50% solution.