Question

A scientist needs 15L of a 38% acid. She mixes together solutions of 30% acid and 40% acid. How much of each solution should she use?

Answer 1

To calculate how much of each solution the scientist should use, we can set up an equation using the concentrations of acid in the solutions. Solving this equation will give us the amounts of the two solutions needed.

Step-by-step explanation:

Let's assume that the scientist needs to use x liters of the 30% acid solution and (15 - x) liters of the 40% acid solution.

Since the concentration of acid in the first solution is 30%, the amount of acid in this solution is 0.30x liters.

The concentration of acid in the second solution is 40%, so the amount of acid in this solution is 0.40(15 - x) liters.

Since the scientist needs 15 liters of a 38% acid solution, the total amount of acid in the final solution is 0.38 * 15 liters.

Equating the amount of acid in the final solution to the sum of the amounts of acid in the two solutions, we get the equation:

0.30x + 0.40(15 - x) = 0.38 * 15

Solving this equation will give us the values of x and (15 - x), which represent the amounts of the two solutions that the scientist should use.