Question

Sam needs a 20% acid solution, but she has only an 18% solution and a 25% solution. she decides to use 100 ml of the 18% solution, and she needs to know how much of the 25% solution she should add.

which equation represents this situation? let x represent the number of milliliters she should add.

Answer 1

Sam needs to set up an equation that equals the total amount of acid from the 18% and 25% solutions to the amount in the final 20% solution. By multiplying the percentage by the volume, we arrive at an equation that can be solved for x, the amount of 25% solution needed.

Step-by-step explanation:

To solve this problem, we use the concept of mixtures in percentages to create the desired concentration of a solution. We know that the amount of pure acid in the final mixture must be the same as the sum of the amount of pure acid in each of the solutions mixed together. Here, let x represent the number of milliliters of the 25% solution that Sam needs to add to the 100 ml of the 18% solution to achieve a 20% solution.

The equation representing the total amount of pure acid in the final solution will equate to the amount in each of the solutions added together:

(0.18)(100) + (0.25)(x) = (0.20)(100 + x)

We multiply the concentration percentage by the volume to find the amount of acid in each solution, and then set that equal to the total amount of acid in the final solution. We can then solve for x to find the amount of 25% solution Sam needs.