Question

Кувшин уравновешивает графин и стакан, 2 кувшина весят столько же, сколько 3 чашки, а стакан и чашка уравновешивают графин. Сколько стаканов уравновешивают графин?

Answer 1

Запишем всё начальными буквами:
К=Г+С
2К=3Ч
Г=С+Ч
из последнего видно, что нужно узнать значение Ч
Ч=2К/3, или Ч=(2*(Г+С))/3
теперь решаем Г=С+(2Г+2С)/3
умножаем обе части на 3: 3Г=3С+2Г+2С
получаем 3Г-2Г=5С ; Г=5С
Ответ: 5 стаканов

Answer 2

Problem Analysis

We are given the following information: - A pitcher balances a carafe and a glass. - Two pitchers weigh the same as three cups. - A glass and a cup balance a carafe.

We need to determine how many glasses balance a carafe.

Solution

Let's assign variables to the unknown quantities: - Let P represent the weight of the pitcher. - Let C represent the weight of a cup. - Let G represent the weight of a glass. - Let Ca represent the weight of the carafe.

From the given information, we can write the following equations: 1. P = Ca + G (The pitcher balances the carafe and the glass) 2. 2P = 3C (Two pitchers weigh the same as three cups) 3. G + C = Ca (A glass and a cup balance a carafe)

We can solve these equations to find the values of G and Ca.

Solving the Equations

Let's solve the equations step by step:

From equation 2, we can express P in terms of C: P = (3C) / 2

Substituting this value of P into equation 1: (3C) / 2 = Ca + G

Rearranging the equation: Ca = (3C) / 2 - G ---(Equation 4)

Substituting the value of Ca from equation 4 into equation 3: G + C = (3C) / 2 - G

Simplifying the equation: 2G + 2C = 3C

Rearranging the equation: G = C

So, we have found that the weight of a glass is equal to the weight of a cup.

Now, let's substitute this value of G into equation 4: Ca = (3C) / 2 - C

Simplifying the equation: Ca = C / 2

Therefore, the weight of the carafe is half the weight of a cup.

Conclusion

From our calculations, we have determined that the weight of the carafe is half the weight of a cup. Therefore, one glass balances a carafe.

Please note that the given problem does not provide specific numerical values for the weights of the pitcher, cup, glass, and carafe. The solution is based on the relationships between these weights as described in the problem statement.

Let me know if you need any further assistance!