Question

За две ручки и пять общих тетрадей заплатили 618 руб. Сколько стоит одна ручка и одна тетрадь, если известно, что 3 ручки дешевле, чем 20 общих тетрадей на 80 руб?

Answer 1

Вместо 80 я написал 8 (это упущение ). 
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Стоимость ручки x руб ,  стоимость тетради у руб.
Можно написать систему :
{2x+5y =618; 20y -3x =80. { 8x+20y =4*618 ; -3x +20y =80 .
11x =4*618 - 80 ;
11x =2392 ;
x =[217] (5/11) (руб).
y=(3x+80)/20 =( (2392/11)*3+80)/20 =(2392*3+11*80)/(11*20) = [36] (34/55) (руб).
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раньше (при разности 8 руб)  получилось 
x=224;
y=34.

Answer 2

Problem Analysis

We are given the information that two pens and five notebooks were purchased for a total of 618 rubles. We need to determine the cost of one pen and one notebook. Additionally, we are given the information that three pens are cheaper than 20 notebooks by 80 rubles.

Solution

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

From the given information, we can form the following equations:

Equation 1: 2x + 5y = 618 (since two pens and five notebooks were purchased for a total of 618 rubles)

Equation 2: 3x = 20y - 80 (since three pens are cheaper than 20 notebooks by 80 rubles)

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

Multiplying Equation 2 by 2, we get:

6x = 40y - 160

Now, we can subtract Equation 1 from this modified Equation 2:

6x - 2x = 40y - 160 - (2x + 5y)

Simplifying the equation:

4x = 35y - 160

Now, we have a new equation:

Equation 3: 4x - 35y = -160

We can solve Equations 1 and 3 simultaneously to find the values of x and y.

Solving the Equations

Let's solve Equations 1 and 3 using the elimination method.

Multiplying Equation 1 by 4, we get:

8x + 20y = 2472

Now, we can subtract Equation 3 from this modified Equation 1:

8x + 20y - (4x - 35y) = 2472 - (-160)

Simplifying the equation:

8x + 20y - 4x + 35y = 2472 + 160

Combining like terms:

4x + 55y = 2632

Now, we have a new equation:

Equation 4: 4x + 55y = 2632

We have a system of two equations: Equation 3: 4x - 35y = -160 Equation 4: 4x + 55y = 2632

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

Solving the System of Equations

To solve the system of equations, we can subtract Equation 3 from Equation 4:

(4x + 55y) - (4x - 35y) = 2632 - (-160)

Simplifying the equation:

4x + 55y - 4x + 35y = 2632 + 160

Combining like terms:

90y = 2792

Solving for y:

y = 2792 / 90

Calculating the value of y:

y ≈ 31.02

Now, we can substitute the value of y back into Equation 1 to find the value of x:

2x + 5(31.02) = 618

Simplifying the equation:

2x + 155.1 = 618

Subtracting 155.1 from both sides:

2x = 618 - 155.1

Calculating the value of x:

x ≈ 231.45

Answer

Based on the calculations, the approximate cost of one pen is 231.45 rubles and the approximate cost of one notebook is 31.02 rubles.

Please note that these values are approximate due to rounding during the calculations.

Let me know if there's anything else I can help you with!