Question

Известно,что 11 одинаковых книг стоят дороже 2050 рублей,а 13 таких же книг стоят дешевле 2440 рублей. Сколько стоит одна книга,если известно,что цена выражается целым числом рублей

Answer 1

Цена 1 книги m∈N
11m>2050   m>2050/11=186 округленно
13m<2440   m<2440/13 = 188

m=187  11m=2057>2050
              13m=2431<2440

книга стоит 187 руб.

Answer 2

Problem Analysis

We are given that 11 identical books cost more than 2050 rubles and 13 identical books cost less than 2440 rubles. We need to find the cost of one book, knowing that the price is expressed as a whole number of rubles.

Solution

Let's assume the cost of one book is x rubles.

From the given information, we can form the following equations: - 11x > 2050 - 13x < 2440

To find the value of x, we need to solve these equations.

Solving the Equations

Let's solve the first equation: 11x > 2050

Dividing both sides of the equation by 11: x > 2050 / 11

Calculating the value: x > 186.36

Since the price is expressed as a whole number of rubles, the minimum value of x is 187.

Now, let's solve the second equation: 13x < 2440

Dividing both sides of the equation by 13: x < 2440 / 13

Calculating the value: x < 187.69

Since the price is expressed as a whole number of rubles, the maximum value of x is 187.

Therefore, the cost of one book is 187 rubles.

Conclusion

The cost of one book is 187 rubles.