Question

В библиотеке пересчитали книги на узбекском и русском языке. Книги на узбекском языке состовляют 20% книг,а если добавить 100 книг на узбекском языке, то их количество будет состовлять 30% книг. Сколько книг на узбекском языке было в библиотеке?

Answer 1

Пусть в библиотеке х книг. Из них 20% на узбекском языке. 

20% от х=0,2х

Если добавить 100 узбекских книг, их  станет 0,2х+100

Всего книг стало х+100

По условию 

$\frac{0,2x+100}{x+100} =0,3$ 

0,3•x+30=0,2x+100

0,1x=70

x=700 (книг всего)

0,2х=140( книг было на узбекском языке)

Проверка. 

140:700=0,2 = 20%

(140+100):(700+100)=240:800=0,3=30%

Answer 2

Calculation of Books in the Library

To calculate the number of books in the library, we need to use the given information. Let's break it down step by step:

1. The books in the library are in two languages: Uzbek and Russian. 2. Initially, the books in Uzbek language make up 20% of the total number of books in the library. 3. If 100 additional books in Uzbek language are added, the percentage of Uzbek books increases to 30%.

Calculation

Let's assume the total number of books in the library is represented by the variable x.

According to the given information: - Initially, the number of books in Uzbek language is 20% of x. - If 100 additional books in Uzbek language are added, the number of Uzbek books becomes 30% of the total number of books.

Based on these conditions, we can set up the following equation:

(0.2 * x) + 100 = 0.3 * (x + 100)

Now, let's solve this equation to find the value of x, which represents the total number of books in the library.

Solving the Equation

Expanding the equation:

0.2x + 100 = 0.3x + 30

Rearranging the terms:

0.2x - 0.3x = 30 - 100