Question

На двух полках стоит 185 книг на второй на 27 книг больше чем на первой решить двумя способами

Answer 1

1)
185-27=158
158:2=79 на первой полке
79+27=106 книг на второй полке
2)
185-27=158
158:2=79. книг на 1 полке
185-79=106

Answer 2

Problem Statement

На двух полках стоит 185 книг, на второй на 27 книг больше, чем на первой. Необходимо решить задачу двумя способами.

Solution 1: Algebraic Approach

Let's assume that the number of books on the first shelf is x. According to the problem, the number of books on the second shelf is 27 more than the number on the first shelf. So, the number of books on the second shelf can be represented as x + 27.

The total number of books on both shelves is given as 185. Therefore, we can write the equation:

x + (x + 27) = 185

Simplifying the equation:

2x + 27 = 185

Subtracting 27 from both sides:

2x = 158

Dividing both sides by 2:

x = 79

So, there are 79 books on the first shelf.

To find the number of books on the second shelf, we substitute the value of x into the equation:

x + 27 = 79 + 27 = 106

Therefore, there are 106 books on the second shelf.

Solution 2: Trial and Error Approach

Another way to solve this problem is by using a trial and error approach. We can start by assuming different numbers for the books on the first shelf and check if it satisfies the given conditions.

Let's assume there are 80 books on the first shelf. According to the problem, the number of books on the second shelf is 27 more than the number on the first shelf. So, on the second shelf, there would be 80 + 27 = 107 books.

Checking the total number of books: 80 + 107 = 187. Since this is not equal to the given total of 185, our assumption is incorrect.

Let's try another assumption. Assuming there are 79 books on the first shelf, the number of books on the second shelf would be 79 + 27 = 106.

Checking the total number of books: 79 + 106 = 185. This satisfies the given condition.

Therefore, the correct solution is that there are 79 books on the first shelf and 106 books on the second shelf.

Conclusion

There are two ways to solve the problem: 1. Algebraic Approach: - Number of books on the first shelf: 79 - Number of books on the second shelf: 106

2. Trial and Error Approach: - Number of books on the first shelf: 79 - Number of books on the second shelf: 106

Both methods yield the same result.