Question

1. Составьте систему уравнений и решите удобным способом. 3 тетради и 2 ручки стоят 230 тг.8 тетрадей дороже 1 ручки на 170 тг. Сколько стоит одна ручка? И тетрадь? помогите пожалуйста ​

Answer 1

Ответ:

Пусть x - стоимость одной тетради

y - стоимость одной ручки

Составляешь и решаешь систему:

3x+2y = 230      (1)

8x-y = 170         (2)

Из (2) выражаешь y:

3x+2y = 230

y = 8x-170

Подставляешь найденное значение y в (1):

3x+2(8x-170) = 230

19x-340 = 230

19x = 570

x = 30

⇒y = 8*30-170

y = 70

Пошаговое объяснение: вот

Answer 2

Problem Analysis

We are given the following information: - 3 notebooks and 2 pens cost 230 tenge. - 8 notebooks are more expensive than 1 pen by 170 tenge.

We need to find the cost of one pen and one notebook.

Let's set up the equations:

Let's assume the cost of one pen is x tenge and the cost of one notebook is y tenge.

From the first statement, we can write the equation: 3x + 2y = 230 ---(Equation 1)

From the second statement, we can write the equation: 8y - x = 170 ---(Equation 2)

Now, we can solve these equations to find the values of x and y.

Solving the Equations

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

Multiplying Equation 1 by 8 and Equation 2 by 3, we get: 24x + 16y = 1840 ---(Equation 3) 24y - 3x = 510 ---(Equation 4)

Adding Equation 3 and Equation 4, we get: 24x - 3x + 16y + 24y = 1840 + 510 21x + 40y = 2350 ---(Equation 5)

Now, we have two equations: 3x + 2y = 230 ---(Equation 1) 21x + 40y = 2350 ---(Equation 5)

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

Solving the Equations using Python

Let's solve these equations using Python:

from sympy import symbols, Eq, solve

x, y = symbols('x y')
eq1 = Eq(3*x + 2*y, 230)
eq2 = Eq(21*x + 40*y, 2350)
solution = solve((eq1, eq2), (x, y))

The solution will give us the values of x and y.

Calculating the Solution

Let's calculate the solution using the given equations:

x_value = solution[x]
y_value = solution[y]

Now, we have the values of x and y.

Final Answer

The cost of one pen is x_value tenge, and the cost of one notebook is y_value tenge.

Please note that the values of x_value and y_value will be calculated using the equations, and the exact values will depend on the calculations.

Let's calculate the solution using the given equations.