Question

Имеются три раствора уксусной эссенции: 8%-ный, 14%-ный и 6%-ный. Если смешать первый и второй растворы, то получится 12%-ный раствор уксусной эссенции. Если смешать первый и третий растворы, то получится 6,5%-ный раствор уксусной эссенции. Каково процентное содержание уксусной эссенции в растворе, полученном путём смешения всех трёх данных растворов?

Answer 1

Пусть растворы будут  x y z
0.08x+014y=0.12x+012y      0.04x=0.02y то есть второго раствора
в 2 раза больше чем первого.
0,08x+0.06z= 0.065x+0.065z      0.015x=0.005z  то есть третьего раствора в три раза  больше чем первого.  чтоб было легче понять:  пусть 1-100  2-200 3-300
все три вместе 600  в 1-8  2-28  3-18  (уксуса) во всех трёх вместе  54      54 от 600 это 9%
ответ:  9%

Answer 2

Calculation of the Percentage of Acetic Acid in the Mixture

To calculate the percentage of acetic acid in the mixture obtained by combining the three given solutions, we can use the information provided about the resulting concentrations.

Let's assign variables to the concentrations of the three solutions: - Let x represent the concentration of the 8% acetic acid solution. - Let y represent the concentration of the 14% acetic acid solution. - Let z represent the concentration of the 6% acetic acid solution.

According to the given information, when the first and second solutions are mixed, a 12% acetic acid solution is obtained. This can be expressed as the following equation:

0.08x + 0.14y = 0.12(x + y) Similarly, when the first and third solutions are mixed, a 6.5% acetic acid solution is obtained. This can be expressed as the following equation:

0.08x + 0.06z = 0.065(x + z) To find the percentage of acetic acid in the mixture obtained by combining all three solutions, we need to solve these two equations simultaneously.

Let's solve the equations:

Equation 1: 0.08x + 0.14y = 0.12x + 0.12y 0.02y = 0.04x y = 2x

Equation 2: 0.08x + 0.06z = 0.065x + 0.065z 0.015z = 0.015x z = x

Now, we can substitute the values of y and z into Equation 1 to find the value of x:

0.02(2x) = 0.04x 0.04x = 0.04x x can be any value

Since x can be any value, we can choose a convenient value to calculate the percentage of acetic acid in the mixture. Let's assume x = 100, which represents a 100% solution.

Using this assumption, we can calculate the values of y and z:

y = 2x = 2(100) = 200 z = x = 100

Therefore, the concentrations of the three solutions are: - 8% acetic acid solution: 100% - 14% acetic acid solution: 200% - 6% acetic acid solution: 100%

To find the percentage of acetic acid in the mixture obtained by combining all three solutions, we can calculate the weighted average of the concentrations:

Percentage of acetic acid in the mixture = (0.08 * 100 + 0.14 * 200 + 0.06 * 100) / (100 + 200 + 100)

Calculating this expression gives us:

(8 + 28 + 6) / 400 = 42 / 400 = 0.105

Therefore, the percentage of acetic acid in the mixture obtained by combining all three solutions is 10.5%.

Please note that the assumption of x = 100 was made for convenience in calculations. The actual values of x, y, and z can vary as long as they satisfy the given equations.