How many milimiters of pure acid must be added to 150 milimiters of a 30% solution of acid to obtain a 40% solution?

I know that the answer is 25 milileters. Could someone show me with steps how to get the answer.

To find out how many milliliters of pure acid must be added to the 150 milliliters of a 30% solution to obtain a 40% solution, you can use the concept of mixture problems.

Step 1: Understand the problem
In this problem, you have 150 milliliters of a 30% acid solution. This means that in these 150 milliliters, 30% of the volume is acid, while the remaining 70% is a solvent or diluent. You want to find out how much pure acid needs to be added to this solution to increase the acid concentration to 40%.

Step 2: Set up the equation
Let's assume that x represents the volume (in milliliters) of pure acid that needs to be added. The equation can be set up as follows:
0.30 * 150 + 1.00 * x = 0.40 * (150 + x)

In this equation, 0.30 * 150 represents the amount of acid in the initial solution, 1.00 * x represents the amount of acid added (pure acid), and 0.40 * (150 + x) represents the amount of acid in the final solution.

Step 3: Solve the equation
Simplifying the equation:
45 + x = 60 + 0.40x

Grouping the x terms:
x - 0.40x = 60 - 45
0.60x = 15

Dividing both sides by 0.60:
x = 15 / 0.60
x = 25

Step 4: Interpret the result
The result indicates that you need to add 25 milliliters of pure acid to the 150 milliliters of a 30% solution in order to obtain a 40% solution.

Therefore, the answer is indeed 25 milliliters.