Question

1 тетрадь, 2 альбома и 3 линейки стоят 48 руб. 3 тетради, 2 альбома и 1 линейка стоят 32 руб. Сколько стоит набор из 1 тетради, 1 альбома и 1 линейки?

Answer 1

48 + 32 = 80 руб - стоят 4 тетради, 4 альбома и 4 линейки

80 : 4 = 20 руб - стоит набор из 1 тетради, 1 альбома и 1 линейки

Answer 2

Calculation of the Cost of the Set

To calculate the cost of the set consisting of 1 notebook, 1 album, and 1 ruler, we can use the given information about the prices of different combinations of items.

According to the information provided: - 1 notebook, 2 albums, and 3 rulers cost 48 rubles. - 3 notebooks, 2 albums, and 1 ruler cost 32 rubles.

Let's assign variables to the prices of each item: - Let x represent the price of 1 notebook. - Let y represent the price of 1 album. - Let z represent the price of 1 ruler.

Based on the given information, we can set up the following equations:

Equation 1: 1x + 2y + 3z = 48 Equation 2: 3x + 2y + 1z = 32

To solve this system of equations, we can use various methods such as substitution or elimination. Let's use the elimination method to find the values of x, y, and z.

Multiplying Equation 1 by 3 and Equation 2 by 1, we get:

Equation 3: 3x + 6y + 9z = 144 Equation 4: 3x + 2y + 1z = 32

Subtracting Equation 4 from Equation 3, we eliminate the variable x:

(3x + 6y + 9z) - (3x + 2y + 1z) = 144 - 32 4y + 8z = 112

Dividing both sides of the equation by 4, we get:

y + 2z = 28

Now, we have two equations:

Equation 5: y + 2z = 28 Equation 6: 3x + 2y + 1z = 32

Multiplying Equation 5 by 2, we get:

2y + 4z = 56

Subtracting Equation 6 from Equation 5, we eliminate the variable y:

(2y + 4z) - (3x + 2y + 1z) = 56 - 32 2z - 3x = 24

Dividing both sides of the equation by 2, we get:

z - (3/2)x = 12

Now, we have two equations:

Equation 7: z - (3/2)x = 12 Equation 8: y + 2z = 28

To solve this system of equations, we need one more equation. Unfortunately, the given information does not provide any additional equations. Therefore, we cannot determine the exact values of x, y, and z, and subsequently, the cost of the set consisting of 1 notebook, 1 album, and 1 ruler.

However, we can express the cost of the set in terms of the variables x, y, and z. Let's solve Equation 7 for z:

z = (3/2)x + 12

Substituting this value of z into Equation 8, we can express y in terms of x:

y = 28 - 2((3/2)x + 12) y = 28 - 3x - 24 y = 4 - 3x

Therefore, the cost of the set consisting of 1 notebook, 1 album, and 1 ruler can be expressed as:

Cost = x + y + z = x + (4 - 3x) + ((3/2)x + 12)

Unfortunately, without additional information or values for x, y, and z, we cannot determine the exact cost of the set.