Question

A scientist needs 120 mL of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. how many milliliters of a 25% solution and how many milliliters of the 10% solution should the scientist make to make the 20% solution ?

Answer 1

Let x be the number of milliliters of the 25% acid solution needed, and y be the number of milliliters of the 10% acid solution needed to make 120 mL of a 20% acid solution.

We can set up a system of two equations based on the information given:

Equation 1: x + y = 120 (total volume of the solution is 120 mL)

Equation 2: 0.25x + 0.1y = 0.2(120) (total amount of acid in the solution is 20% of 120 mL)

Simplifying Equation 2, we get:

0.25x + 0.1y = 24

Now we can use Equation 1 to solve for one of the variables in terms of the other. Let's solve for y:

y = 120 - x

Substituting this into Equation 2, we get:

0.25x + 0.1(120 - x) = 24

Simplifying and solving for x, we get:

0.25x + 12 - 0.1x = 24

0.15x = 12

x = 80

So we need 80 mL of the 25% acid solution. Using Equation 1 to find y, we get:

y = 120 - x = 120 - 80 = 40

So we need 40 mL of the 10% acid solution.

Therefore, the scientist needs to mix 80 mL of the 25% acid solution and 40 mL of the 10% acid solution to obtain 120 mL of a 20% acid solution.