Question

На двух книжных полках было 68 книг. После того как с одной полки на другую переложили 9 книг, на первой полке оказалось в 3 раза меньше, чем на второй. Сколько книг было на каждой полке первоначально?

Answer 1

Пусть на первой полке х книг, тогда на второй (68-х) книг. После того как с первой полки переложили 9 книг, на первой полке стало (х-9) книг, а на второй полке стало (68-х)+9 книг. По условию (х-9) в три раза меньше, чем (68-х)+9. Составляем уравнение 3·(х-9)=(68-х)+9 3х-27=68-х+9 3х+х=68+9+27 4х=104 х=26 68-х=68-26=42 Ответ. На первой полке 26 книг, на второй 42.

Answer 2

Problem Analysis

We are given that there are 68 books on two bookshelves. After transferring 9 books from one shelf to the other, the number of books on the first shelf becomes three times smaller than the number of books on the second shelf. We need to determine the initial number of books on each shelf.

Solution

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

According to the given information, after transferring 9 books from one shelf to the other, the number of books on the first shelf becomes three times smaller than the number of books on the second shelf. Mathematically, this can be represented as:

x - 9 = (y - 9) / 3 We also know that the total number of books on both shelves is 68. Mathematically, this can be represented as:

x + y = 68 We can solve these two equations simultaneously to find the values of x and y.

Solving the Equations

Let's solve the equations using the substitution method.

From equation 2, we can express x in terms of y:

x = 68 - y Substituting this value of x into equation 1:

68 - y - 9 = (y - 9) / 3

Simplifying the equation:

59 = (y - 9) / 3

Multiplying both sides by 3:

177 = y - 9

Adding 9 to both sides:

y = 186

Substituting this value of y into equation 2:

x + 186 = 68

Subtracting 186 from both sides:

x = -118

Since the number of books cannot be negative, we discard the solution x = -118.

Therefore, the initial number of books on the first shelf is x = 68 - y = 68 - 186 = -118.

Conclusion

Based on the given information, it is not possible to determine the initial number of books on each shelf. The solution obtained for the initial number of books on the first shelf is negative, which is not valid in this context.