Question

Два сосуда были наполнены растворами соли, причём в первом сосуде содержалось на 1 л меньше раствора, чем во втором. Концентрация раствора в первом сосуде составляла 10%, а во втором - 20%. После того как растворы слили в третий сосуд, получили новый раствор, концентрация которого составила 16%. Сколько раствора было в каждом сосуде первоначально?

Answer 1

х л раствора в 1 сосуде

х + 1 л раствора во 2 сосуде

х + х + 1 = 2х + 1 л раствора получили в 3 сосуде

0,1х концентрация соли в 1 растворе

0,2(х+1) концентрация соли во 2 растворе

0,16(2х + 1) концентрация соли в 3 растворе

0,1х + 0,2(х+1) = 0,16(2х + 1)

0,1х + 0,2х + 0,2 = 0,32х + 0,16

0,32х - 0,3х = 0,2 - 0,16

0,02х = 0,04

х = 2

2 л раствора в 1 сосуде

2 + 1 = 3 л раствора во 2 сосуде

Answer 2

Problem Analysis

We are given two vessels filled with salt solutions. The concentration of the solution in the first vessel is 10%, while the concentration in the second vessel is 20%. After the solutions are mixed in a third vessel, the concentration of the resulting solution is 16%. We need to determine the initial amount of solution in each vessel.

Solution

Let's assume that the initial volume of the solution in the first vessel is x liters. Since the second vessel contains 1 liter more than the first vessel, the initial volume of the solution in the second vessel is x + 1 liters.

To find the amount of salt in each vessel, we can multiply the volume of the solution by its concentration. The amount of salt in the first vessel is 0.1x liters, and the amount of salt in the second vessel is 0.2(x + 1) liters.

When the solutions are mixed, the total volume of the resulting solution is 2x + 1 liters. The amount of salt in the resulting solution is the sum of the amounts of salt in the first and second vessels, which is 0.1x + 0.2(x + 1) liters.

According to the problem, the concentration of the resulting solution is 16%. We can express this as the ratio of the amount of salt to the total volume of the solution:

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

To solve this equation, we can simplify it by multiplying both sides by (2x + 1):

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

Simplifying further:

0.32x + 0.16 = 0.1x + 0.2x + 0.2

Combining like terms:

0.32x + 0.16 = 0.3x + 0.2

Subtracting 0.3x from both sides:

0.02x + 0.16 = 0.2

Subtracting 0.16 from both sides:

0.02x = 0.04

Dividing both sides by 0.02:

x = 2

Therefore, the initial volume of the solution in the first vessel is 2 liters, and the initial volume of the solution in the second vessel is 3 liters.

Answer

The initial volume of the solution in the first vessel was 2 liters, and the initial volume of the solution in the second vessel was 3 liters.