Question

Комплект из открытки,конверта,и блокнота стоит 50 руб.конверт на 25 руб дешевле блокнота и в 3 раза дешевле открытки.сколько стоит конверт,открытка и блокнот?

Answer 1

Х-конверт
х+25-блокнот
3х-открытка
х+х+25+3х=50
5х=25
х=25/5=5 руб- конверт
5+25=30р- блокнот
5*3=15р- открытка

Answer 2

Calculation of the Prices

To determine the prices of the envelope, card, and notebook, let's assign variables to each item: - Let x be the price of the envelope. - Let y be the price of the card. - Let z be the price of the notebook.

According to the given information, we have the following equations: 1. The total price of the set is 50 rubles: x + y + z = 50. 2. The envelope is 25 rubles cheaper than the notebook: x = z - 25. 3. The envelope is 3 times cheaper than the card: x = y / 3.

To solve this system of equations, we can substitute the values from equations 2 and 3 into equation 1.

Solving the Equations

Let's substitute z - 25 for x in equation 1: (z - 25) + y + z = 50.

Now, let's substitute y / 3 for x in equation 1: (y / 3) + y + z = 50.

Simplifying the equation: (4y + 3z) / 3 = 50.

Multiplying both sides of the equation by 3 to eliminate the fraction: 4y + 3z = 150.

Now, we have a system of two equations: 1. z - 25 + y + z = 50 2. 4y + 3z = 150

We can solve this system of equations to find the values of y and z.

Solving the System of Equations

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

Multiplying equation 1 by 4 to eliminate y: 4z - 100 + 4y + 4z = 200.

Simplifying the equation: 8z + 4y = 300.

Now, we have the following system of equations: 1. 8z + 4y = 300 2. 4y + 3z = 150

Multiplying equation 2 by 2 to eliminate y: 8y + 6z = 300.

Now, we have the following system of equations: 1. 8z + 4y = 300 2. 8y + 6z = 300

Subtracting equation 2 from equation 1 to eliminate y: (8z + 4y) - (8y + 6z) = 300 - 300.

Simplifying the equation: 2z - 4y = 0.

Dividing both sides of the equation by 2: z - 2y = 0.

Now, we have the following system of equations: 1. z - 2y = 0 2. 8y + 6z = 300

Let's solve this system of equations.

Solving the Updated System of Equations

Multiplying equation 1 by 6 to eliminate z: 6z - 12y = 0.

Now, we have the following system of equations: 1. 6z - 12y = 0 2. 8y + 6z = 300

Adding equation 1 to equation 2 to eliminate z: (6z - 12y) + (8y + 6z) = 0 + 300.

Simplifying the equation: 14z - 4y = 300.

Dividing both sides of the equation by 2: 7z - 2y = 150.

Now, we have the following system of equations: 1. 7z - 2y = 150 2. 8y + 6z = 300

Multiplying equation 1 by 3 to eliminate y: 21z - 6y = 450.

Now, we have the following system of equations: 1. 21z - 6y = 450 2. 8y + 6z = 300

Adding equation 1 to equation 2 to eliminate y: (21z - 6y) + (8y + 6z) = 450 + 300.

Simplifying the equation: 27z = 750.

Dividing both sides of the equation by 27: z = 27.78.

Now, we have the value of z (the price of the notebook).

Substituting z = 27.78 into equation 2 to find y: 8y + 6(27.78) = 300.

Simplifying the equation: 8y + 166.68 = 300.

Subtracting 166.68 from both sides of the equation: 8y = 133.32.

Dividing both sides of the equation by 8: y = 16.665.

Now, we have the value of y (the price of the card).

Substituting y = 16.665 into equation 3 to find x: x = y / 3 = 16.665 / 3 = 5.555.

Now, we have the value of x (the price of the envelope).

Final Answer

After solving the system of equations, we found the following prices: - The price of the envelope (x) is approximately 5.555 rubles. - The price of the card (y) is approximately 16.665 rubles. - The price of the notebook (z) is approximately 27.78 rubles.

Therefore, the envelope, card, and notebook cost approximately 5.555 rubles, 16.665 rubles, and 27.78 rubles, respectively.