Question

За 2 блокнота 5 карандашей и 3 ручки заплатили 119рублей.Найди цену блокнота,карандаша и ручки если за 2 блокнота 5 карандашей заплатили 83 рубля,а за 5 карандашей и 3 ручки -8 рублей.

Answer 1

5х+3х=8

8х=8

х=8:8=1руб значит карандаш и ручка стоят по 1 рублю

5х1=5 руб заплатили за 5 карандашей

83-5=78руб стоят 2 блокнота

78:2=39 руб стоит 1 блокнот

Ответ:блокнот стоит 39руб,карандаш и ручка стоят по 1рублю.

проверим: 39х2+5х1=83рубля стоят 2 блокнота и 5 карандашей

                 5х1+3х1=8 рублей стоят 5карандашей и 3 ручки

                 119 рублей не получается,может опечатка? 

 

Answer 2

Calculation of Prices for Notebooks, Pencils, and Pens

To find the prices of notebooks, pencils, and pens, we can set up a system of equations based on the given information.

Let's assume the price of a notebook is x rubles, the price of a pencil is y rubles, and the price of a pen is z rubles.

From the given information, we have the following equations:

Equation 1: 2x + 5y + 3z = 119 rubles Equation 2: 2x + 5y = 83 rubles Equation 3: 5y + 3z = -8 rubles

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

Solving the System of Equations

We'll start by eliminating the variable x from equations 2 and 3.

Multiplying equation 2 by 3, we get: 6x + 15y = 249 rubles (equation 4)

Multiplying equation 1 by 2, we get: 4x + 10y + 6z = 238 rubles (equation 5)

Now, subtracting equation 4 from equation 5, we can eliminate x: (4x + 10y + 6z) - (6x + 15y) = 238 - 249 -2x - 5y + 6z = -11 rubles (equation 6)

Next, we'll eliminate the variable y from equations 6 and 3.

Multiplying equation 6 by 5, we get: -10x - 25y + 30z = -55 rubles (equation 7)

Multiplying equation 3 by 2, we get: 10y + 6z = -16 rubles (equation 8)

Adding equation 7 and equation 8, we can eliminate y: (-10x - 25y + 30z) + (10y + 6z) = -55 - 16 -10x + 6z = -71 rubles (equation 9)

Now, we have two equations with two variables:

Equation 9: -10x + 6z = -71 rubles Equation 1: 2x + 5y + 3z = 119 rubles

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

Solving the System of Equations

To solve the system of equations, we can use the substitution method.

From equation 9, we can express x in terms of z: -10x = -71 - 6z x = (71 + 6z) / 10

Substituting this value of x into equation 1, we get: 2((71 + 6z) / 10) + 5y + 3z = 119

Simplifying the equation, we have: (71 + 6z) / 5 + 5y + 3z = 119 (71 + 6z) + 25y + 15z = 595 71 + 6z + 25y + 15z = 595 41z + 25y = 524 (equation 10)

Now, we have two equations with two variables:

Equation 10: 41z + 25y = 524 Equation 3: 5y + 3z = -8

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 the substitution method.

From equation 3, we can express y in terms of z: 5y = -8 - 3z y = (-8 - 3z) / 5

Substituting this value of y into equation 10, we get: 41z + 25((-8 - 3z) / 5) = 524

Simplifying the equation, we have: 41z - 40 - 15z = 524 26z = 564 z = 564 / 26 z ≈ 21.69

Now, we have the value of z. We can substitute it back into equation 3 to find the value of y:

5y + 3(21.69) = -8 5y + 65.07 = -8 5y = -8 - 65.07 5y = -73.07 y = -73.07 / 5 y ≈ -14.61

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

2x + 5(-14.61) + 3(21.69) = 119 2x - 73.05 + 65.07 = 119 2x - 7.98 = 119 2x = 119 + 7.98 2x = 126.98 x = 126.98 / 2 x ≈ 63.49

Therefore, the approximate prices are: - The price of a notebook is 63.49 rubles. - The price of a pencil is -14.61 rubles. - The price of a pen is 21.69 rubles.

Please note that the negative price for a pencil may indicate an error in the given information or calculations. It is unusual for a price to be negative.

Answer 3

Предположим, что цена блокнота обозначается как "х" рублей, цена карандаша - "у" рублей, а цена ручки - "z" рублей.

Из условия задачи у нас есть два уравнения:

1) 2х + 5у + 3z = 119 2) 2х + 5у = 83 3) 5у + 3z = 8

Решим систему уравнений:

Из уравнения (2) выразим 2х: 2х = 83 - 5у

Подставим это значение в уравнение (1): (83 - 5у) + 5у + 3z = 119 83 + 3z = 119 3z = 119 - 83 3z = 36 z = 12

Теперь подставим значение z в уравнение (3): 5у + 36 = 119 5у = 119 - 36 5у = 83 у = 16.6

Теперь, когда мы знаем значения y и z, можем найти значение x из уравнения (2): 2х + 5*16.6 = 83 2х + 83 = 83 2х = 0 x = 0

Теперь у нас есть значения x, y и z: x = 0 рублей (цена блокнота) y = 16.6 рублей (цена карандаша) z = 12 рублей (цена ручки)

Итак, цена блокнота, карандаша и ручки составляет 0 рублей, 16.6 рублей и 12 рублей соответственно.