Question

На двух книжных полках 92 книги. Если 1/3 кол-во книг со второй полки переложить на первую полку , тогда на первой полке станет на 20 книг больше, чем на второй.Сколько книг было на первой полке?Сколько во второй? составьте систему и решите способом сложения.

Answer 1

Пусть х книг на 1 полке, у на второй
х+у=92
х+1/3у-20=2/3у  

x-1\3y=20  умножим на 3

х+у=92
3х-у=60
сложим
4х=152
х=38 книг на первой
92-38=54 книги на второй

Answer 2

Problem Analysis

We are given that there are 92 books on two bookshelves. If we move 1/3 of the books from the second shelf to the first shelf, the first shelf will have 20 more books than the second shelf. We need to find the number of books on each shelf.

Solution

Let's assume the number of books on the first shelf is x and the number of books on the second shelf is y.

According to the given information, we can set up the following equations:

1. The total number of books on both shelves is 92: x + y = 92 2. If we move 1/3 of the books from the second shelf to the first shelf, the first shelf will have 20 more books than the second shelf: x = y + 20 To solve this system of equations, we can substitute the value of x from equation 2 into equation 1:

y + 20 + y = 92

Simplifying the equation:

2y + 20 = 92

Subtracting 20 from both sides:

2y = 72

Dividing both sides by 2:

y = 36

Now, we can substitute the value of y back into equation 2 to find the value of x:

x = 36 + 20 = 56

Therefore, there were 56 books on the first shelf and 36 books on the second shelf.

Answer

There were 56 books on the first shelf and 36 books on the second shelf.