Question

имеются два сосуда с раствором соли, причём во втором сосуде раствора на 2 литра больше, чем в первом. В первом сосуде содержание соли в растворе составляет 20%, а во втором 50%. Растворы из двух сосудов слили в один. Содержание соли в новом растворе составило 40%. Определите количество раствора, которое было во втором сосуде.

Answer 1

Пусть в первом сосуде было х л раствора,

тогда во втором было х+2 л раствора.

Соли в первом сосуде 0,2х л, а во втором 0,5*(х+2) л.

После слияния двух растворов в один в нём оказалось (х+х+2=2х+2) л, причём содержание соли там оказалось 0,4(2х+2) л.

Составим уравнение:

0,2х+0,5(х+2)=0,4(2х+2)

0,2х+0,5х+1=0,8х+0,8

0,7х-0,8х=0,8-1

-0,1х=-0,2

х=2 (л)-первоначально было в первом сосуде

х+2=2+2=4(л)-первоначально было во втором сосуде

 

Ответ: 4 л

 

 

 

Answer 2

Problem Analysis

We have two vessels containing salt solutions. The second vessel has 2 liters more solution than the first vessel. The concentration of salt in the first vessel is 20%, while in the second vessel it is 50%. When the solutions from both vessels are mixed, the concentration of salt in the resulting solution is 40%. We need to determine the amount of solution in the second vessel.

Solution

Let's assume that the amount of solution in the first vessel is x liters. Since the second vessel has 2 liters more solution, the amount of solution in the second vessel is x + 2 liters.

The concentration of salt in the first vessel is 20%, which means that the amount of salt in the first vessel is 20% of x liters.

The concentration of salt in the second vessel is 50%, which means that the amount of salt in the second vessel is 50% of (x + 2) liters.

When the solutions from both vessels are mixed, the resulting solution has a concentration of 40%. This means that the amount of salt in the resulting solution is 40% of the total amount of solution, which is (x + x + 2) liters.

To solve for x, we can set up the following equation:

(amount of salt in the first vessel + amount of salt in the second vessel) / total amount of solution = concentration of salt in the resulting solution

(0.20 * x + 0.50 * (x + 2)) / (2x + 2) = 0.40

Now we can solve this equation to find the value of x.

Calculation

Let's solve the equation:

(0.20 * x + 0.50 * (x + 2)) / (2x + 2) = 0.40

0.20x + 0.50x + 1.00 = 0.40(2x + 2)

0.20x + 0.50x + 1.00 = 0.80x + 0.80

0.70x + 1.00 = 0.80x + 0.80

0.70x - 0.80x = 0.80 - 1.00

-0.10x = -0.20

x = -0.20 / -0.10

x = 2

Answer

The amount of solution in the second vessel is x + 2 liters, which is equal to 2 + 2 = 4 liters.