Question

(решить с помощью уравнения) В библиотеке книги на французском языке составляют 48% от числа книг на английском языке, а вместе они составляют 5% числа всех книг в библиотеке. Сколько всего книг в библиотеке, если книг на английском языке на 260 больше, чем на французском?

Answer 1

Пусть всего в библиотеке x книг. Тогда книг на английском и французском 0,05x.
Книг на французском 48% от книг на английском. Значит и тех, и других 100%+48% = 148% от количества книг на английском. То есть, книг на английском $0,05x:148\%=0,05x:1,48 =\frac5{148}x$ шт, а книг на французском $0,05x:1,48\cdot0,48=0,024x:1,48=\frac{24}{1480}x$.
Книг на английском на 260 больше, то есть
$\frac{5}{148}x-\frac{24}{1480}x=260\\\frac{50-24}{1480}x=260\\\frac{26}{1480}x=260\\x=260:\frac{26}{1480}\\x=\260\cdot\frac{1480}{26}\\x=10\cdot1480\\x=14800$

В библиотеке всего 14800 книг.

Answer 2

Problem Analysis

To solve this problem, we need to find the total number of books in the library given the following information: - Books in French make up 48% of the total number of books in English. - The combined number of books in French and English is 5% of the total number of books in the library. - The number of books in English is 260 more than the number of books in French.

Let's denote the total number of books in the library as x. We can set up the following equations based on the given information:

1. The number of books in French is 48% of the number of books in English: - Number of books in French = 0.48 * Number of books in English

2. The combined number of books in French and English is 5% of the total number of books in the library: - Number of books in French + Number of books in English = 0.05 * Total number of books

3. The number of books in English is 260 more than the number of books in French: - Number of books in English = Number of books in French + 260

We can solve these equations simultaneously to find the value of x, which represents the total number of books in the library.

Solution

Let's solve the equations step by step:

1. Substitute the value of the number of books in English from equation 3 into equation 1: - 0.48 * (Number of books in French + 260) = Number of books in French

2. Expand the equation: - 0.48 * Number of books in French + 0.48 * 260 = Number of books in French

3. Simplify the equation: - 0.48 * Number of books in French - Number of books in French = -0.48 * 260

4. Combine like terms: - -0.52 * Number of books in French = -0.48 * 260

5. Divide both sides of the equation by -0.52 to solve for the number of books in French: - Number of books in French = (-0.48 * 260) / -0.52

6. Calculate the value of the number of books in French: - Number of books in French ≈ 240

7. Substitute the value of the number of books in French into equation 3 to find the number of books in English: - Number of books in English = 240 + 260

8. Calculate the value of the number of books in English: - Number of books in English = 500

9. Substitute the values of the number of books in French and English into equation 2 to find the total number of books in the library: - 240 + 500 = 0.05 * Total number of books

10. Solve for the total number of books in the library: - Total number of books = (240 + 500) / 0.05

11. Calculate the value of the total number of books in the library: - Total number of books ≈ 14800

Therefore, there are approximately 14,800 books in the library.

Note: The above solution assumes that the percentage values given in the problem are accurate and that there are no other languages or factors involved in the total number of books in the library.