Question

При смешивании первого раствора кислоты, концетрация которого 40 процентов, и второго раствора этой же кислоты, концетрация которого 48 процентов, получили раствор с концетрацией 42 процента. В каком отношении были взяты первый и второй растворы

Answer 1

х - масса первого раствора;

у - масса второго раствора;

тогда в первом р-ре масса к-ты 0,4х , во втором - 0,48у.

Масса всего раствора при смешивании равна (х+у), при этом масса кислоты - 0,48(х+у).

Составим и решим ур-е:

0,4х + 0,48у = 0,42(х+у)   | *100

40х + 48у = 42х +42у

х=3у

Отношение р-ров : х/у = 3у/у = 3:1

Ответ: 3 : 1.

 

Answer 2

Mixing Acid Solutions to Obtain a 42% Concentration Solution

To determine the ratio in which the first and second acid solutions with concentrations of 40% and 48% were mixed to obtain a solution with a concentration of 42%, we can use the following approach:

Let's assume that x liters of the 40% solution and y liters of the 48% solution were mixed to obtain a total of z liters of the 42% solution.

The equation for the concentration of the resulting solution can be expressed as:

0.40x + 0.48y = 0.42z

This equation represents the conservation of acid in the mixing process.

We can also use the fact that the total volume of the resulting solution is the sum of the volumes of the two initial solutions:

x + y = z

Solving these two equations simultaneously will give us the ratio in which the two solutions were mixed.

Let's proceed with the calculations:

0.40x + 0.48y = 0.42z x + y = z

Using these equations, we can solve for the ratio of x to y.

0.40x + 0.48y = 0.42(x + y) 0.40x + 0.48y = 0.42x + 0.42y 0.06y = 0.02x 3y = x

This means that the first solution was used in a 3:1 ratio with the second solution to obtain the desired concentration of 42%.

So, the first and second solutions were mixed in a ratio of 3:1 to achieve the 42% concentration.

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