Question

Послеитого как с первой полки сняли 2 книги а со второй 8 книг га обеих полках осталось 42 книги . Сколько книг было на каждой полке первоначально если на первой осталось больше книг чем на второй

Answer 1

Problem Analysis

We are given that 2 books were removed from the first shelf and 8 books were removed from the second shelf, leaving a total of 42 books on both shelves. We need to determine the initial number of books on each shelf, considering that there were more books left on the first shelf than on the second.

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, we have the following equations:

1. After removing 2 books from the first shelf, the number of books left on the first shelf is x - 2. 2. After removing 8 books from the second shelf, the number of books left on the second shelf is y - 8. 3. The total number of books left on both shelves is 42, so we have the equation (x - 2) + (y - 8) = 42.

We also know that there were more books left on the first shelf than on the second, so we have the equation x - 2 > y - 8.

Now we can solve these equations to find the values of x and y.

Solution Steps

1. Rewrite the equation (x - 2) + (y - 8) = 42 as x + y = 52 by simplifying the equation. 2. Rewrite the equation x - 2 > y - 8 as x - y > -6 by simplifying the equation. 3. Rearrange the equation x + y = 52 to solve for x: x = 52 - y. 4. Substitute the value of x in the equation x - y > -6: 52 - y - y > -6. 5. Simplify the equation: 52 - 2y > -6. 6. Rearrange the equation to solve for y: 2y < 52 + 6. 7. Simplify the equation: 2y < 58. 8. Divide both sides of the equation by 2: y < 29. 9. Since y represents the number of books on the second shelf, the maximum value for y is 28 (since there were more books left on the first shelf). 10. Substitute the value of y in the equation x = 52 - y: x = 52 - 28. 11. Simplify the equation: x = 24.

Therefore, the initial number of books on the first shelf was 24 and the initial number of books on the second shelf was 28.

Answer

The initial number of books on the first shelf was 24 and the initial number of books on the second shelf was 28.