Question

Одна Открытка, 2 одинаковых конверта и 3 одинаковые марки стоят 38 р. Три такие открытки, 2 таких конверта и 1 такая же марка стоят 22 р. Сколько стоит набор из открытки, конверта, и марки? Решите пожалуйста задачу!

Answer 1

Пусть  X - цена открытки
          Y  - цена конверта
          Z - цена марки  ,    тогда :
X + 2*Y + 3*Z = 38      (1)
3*X + 2*Y + Z = 22      (2)
    из (1) вычитаем  (2), получаем:
- 2*X + 2*z =16  или  Z= X +8   подставляем значение  Z в (2) :
3*X + 2*Y +X + 8 =22  или  4*X + 2*Y = 14  или  2*X +Y =7   или Y+ 7 - 2*X
Итак, имеем :   
Z=X + 8  и   Y= 7 - 2*X.   Далее предполагаем реальную цену. Например,
X=2, тогда Z= X+8=10,   Y = 7 - 2*2 = 3    Проверяем, подставляя эти значения в (1) и (2) :
2 + 2*3 + 3*10= 38     ВЕРНО!
3*2 + 2*3 + 10 = 22   ВЕРНО!
2 + 3 + 8 = 13(рублей) - стоимость открытки, конверта и марки.
Ответ:  13 рублей.

Answer 2

Problem Analysis

We are given the following information: - One greeting card, two identical envelopes, and three identical stamps cost 38 rubles. - Three greeting cards, two identical envelopes, and one identical stamp cost 22 rubles.

We need to find the cost of a set consisting of one greeting card, one envelope, and one stamp.

Solution

Let's assume the cost of one greeting card is x rubles, the cost of one envelope is y rubles, and the cost of one stamp is z rubles.

From the given information, we can form the following equations:

Equation 1: x + 2y + 3z = 38 (One greeting card, two envelopes, and three stamps cost 38 rubles)

Equation 2: 3x + 2y + z = 22 (Three greeting cards, two envelopes, and one stamp cost 22 rubles)

To solve these equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can express x in terms of y and z:

x = 38 - 2y - 3z

Substituting this value of x into Equation 2, we get:

3(38 - 2y - 3z) + 2y + z = 22

Simplifying the equation:

114 - 6y - 9z + 2y + z = 22

-4y - 8z = -92

Dividing the equation by -4:

y + 2z = 23

Now we have two equations:

Equation 3: y + 2z = 23

Equation 4: -4y - 8z = -92

We can solve these equations simultaneously to find the values of y and z.

Solving the Equations

To solve the equations, we can use the method of substitution or elimination. Let's use the method of elimination.

Multiplying Equation 3 by 4, we get:

4y + 8z = 92

Adding this equation to Equation 4, we eliminate y:

4y + 8z - 4y - 8z = 92 - (-92)

Simplifying the equation:

0 = 184

This equation is not possible to solve because it results in an inconsistency. It means that there is no solution that satisfies both Equation 3 and Equation 4.

Therefore, there is no unique solution to this problem. The given information is contradictory, and we cannot determine the cost of a set consisting of one greeting card, one envelope, and one stamp.

Please double-check the given information or provide additional details if available.