Question

20 БАЛЛОВ ЗА ЛУЧШИЙ ОТВЕТ!) СРОЧНО НУЖНО СДЕЛАТЬ...Имеются два сосуда, содержащие 20 и 16 кг раствора кислоты различной концентрации. Если их слить вместе, то получим раствор, содержащий 41% кислоты. Если же слить равные массы этих растворов, то полученный раствор будет содержать 43% кислоты. Сколько килограммов кислоты содержится в первом растворе?Пожалуйста, чем подробнее тем лучше.... я не понимаю как ее сделать...

Answer 1

Если концентрация кислоты в первом сосуде х %, тогда во втором у %.  
20*х/100+16*у/100=36*41/100
по второму условию
 20*х/100+20*у/100=40*43/100    на 100 можно не делить, в принципе
 Решаем полученную систему: 
20х+16у=1476 разделим на 4
20х+20у=.1720 разделим на 20
5х+4у=369
х+у=86
х=86-у      подставим
5(86-у)+4у=369
430-5у+4у=369
 у=61%-во втором
х=86-61
х=25%-в первом
Масса кислоты в первом растворе 20*25/100=5 кг.

Answer 2

Problem Analysis

We have two vessels containing solutions of acid with different concentrations. When these solutions are mixed together, a solution with a concentration of 41% acid is obtained. When equal masses of these solutions are mixed, a solution with a concentration of 43% acid is obtained. We need to determine the amount of acid in the first solution.

Solution

Let's assume that the first vessel contains x kg of acid solution with concentration a%, and the second vessel contains y kg of acid solution with concentration b%.

According to the problem, when the two solutions are mixed together, a solution with a concentration of 41% acid is obtained. This can be expressed as:

x * a% + y * b% = (x + y) * 41% Similarly, when equal masses of the two solutions are mixed, a solution with a concentration of 43% acid is obtained. This can be expressed as:

(x / 2) * a% + (y / 2) * b% = (x / 2 + y / 2) * 43% We can solve these two equations to find the values of x and y.

Let's simplify equation by multiplying both sides by 2:

x * a% + y * b% = (x + y) * 43% Now, we have two equations and with the same left-hand side. We can subtract equation from equation to eliminate the common terms:

(x * a% + y * b%) - (x * a% + y * b%) = (x + y) * 41% - (x + y) * 43%

Simplifying further:

0 = (x + y) * 41% - (x + y) * 43%

Factoring out (x + y):

0 = (x + y) * (41% - 43%)

Simplifying:

0 = (x + y) * (-2%)

Since the product of (x + y) and -2% is zero, either (x + y) is zero or -2% is zero. Since -2% cannot be zero, we conclude that (x + y) must be zero.

Therefore, we can conclude that the first solution (x) must be zero, and the second solution (y) must contain all the acid.

Hence, the first solution contains 0 kg of acid.

Answer

The first solution contains 0 kg of acid.

Note: The solution assumes that the concentrations of the acid solutions are expressed as percentages.