Question

Помогите Пожалуйста Решите задачу при помощи уравнения:За 3 ручки и 5 карандашей заплатили 137 рублей. Карандаш дешевле ручки на 11 р. Сколько рублей стоит карандаш? Ручка?​

Answer 1

Ответ:

x - karandash

5x + 3(x+ 11) = 137

5x + 3x + 33 = 137

8x = 102

x = 12.75 rub. - karaandash

12.75 + 11 = 23.75 - ruchka

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given the information that 3 pens and 5 pencils were purchased for a total of 137 rubles. Additionally, we know that the pencils are 11 rubles cheaper than the pens. We need to find the individual prices of the pencils and pens.

Solution

Let's assume the price of a pen is x rubles. Since the pencils are 11 rubles cheaper, the price of a pencil would be (x - 11) rubles.

According to the given information, the total cost of 3 pens and 5 pencils is 137 rubles. We can express this information as an equation:

3x + 5(x - 11) = 137

Now, let's solve this equation to find the value of x.

Solving the Equation

Expanding the equation, we get:

3x + 5x - 55 = 137

Combining like terms, we have:

8x - 55 = 137

Adding 55 to both sides of the equation, we get:

8x = 192

Dividing both sides of the equation by 8, we find:

x = 24

Answer

The price of a pen is 24 rubles. Since the pencils are 11 rubles cheaper, the price of a pencil would be (24 - 11) = 13 rubles.

Therefore, the pen costs 24 rubles and the pencil costs 13 rubles.

Answer 3

Solving the Equation for the Cost of Pencils and Pens

To solve the given problem, we can use a system of equations to represent the given information and then solve for the cost of pencils and pens.

Let's denote the cost of a pencil as x and the cost of a pen as y.

We are given the following information: 1. 3 pens and 5 pencils cost 137 rubles. 2. The cost of a pencil is 11 rubles less than the cost of a pen.

We can represent this information in the form of equations:

1. 3y + 5x = 137 (equation representing the total cost of pens and pencils) 2. x = y - 11 (equation representing the relationship between the cost of a pencil and a pen)

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

Solving the System of Equations

We can start by substituting the value of x from the second equation into the first equation:

3y + 5(y - 11) = 137

Solving for y: 3y + 5y - 55 = 137 8y - 55 = 137 8y = 192 y = 24

Now that we have found the value of y, we can substitute it back into the second equation to find the value of x:

x = 24 - 11 x = 13

Answer:

So, the cost of a pencil is 13 rubles and the cost of a pen is 24 rubles.