Question

Two containers were filled with salt solutions, and the first container contained 1 liter less solution than the second. The mass concentration of salt from the solution in the first container was 10%, and in the second, 20%. After both solutions were poured into the third container, a new solution was obtained, the concentration of which was 16%. How much solution (volume) was in each container initially?

I just wonder how such kind of problems are solved. I'd be very grateful if you help me to understand. It's from 7th grade.

Answer 1

To solve this problem, set up an equation using the given information and solve for the initial volumes of the containers.

Step-by-step explanation:

Let's assume that the volume of the second container is x liters. Therefore, the volume of the first container would be x-1 liters. Now, we can calculate the quantities of salt in each container. In the first container, the volume of salt is 0.1(x-1) liters, and in the second container, the volume of salt is 0.2x liters.

When the solutions from both containers are combined in the third container, the resulting concentration is 0.16. We can set up the equation:

0.1(x-1) + 0.2x = 0.16(2x-1)

Simplifying and solving this equation will give us the initial volumes of the two containers.