Question

Решите задачу арифметическим методом,выполнив модель виде схемы. Проверку сделайте алгебраическим методом. На втором полке на 3 книги больше чем на первой, а на третьей полке на 4 книги больше, чем на второй полке. Всего на трех полках 55 книг. сколько книг на каждом полке?

Answer 1

1 полка ___________ ?
2 полка ___________.+3___  ?
3 полка ________________+4_____  ?
Всего 55
Представим, что книг на всех полках поровну. Чтобы
уравнять количество книг.на всех полках., надо убрать со второй полки 3 книги, а с третьей 4 книги.
1) 3+4=7(к.)
2) 55-7=48(к.) на трёх полках, если их поровну
3)48:3=16 (к.) на первой полке
4)16+3=19(к.) на второй
5) 19+4=23 (к.) на третьей

Answer 2

Problem Analysis

We are given information about the number of books on three shelves. The second shelf has 3 more books than the first shelf, and the third shelf has 4 more books than the second shelf. The total number of books on all three shelves is 55. We need to determine the number of books on each shelf.

Arithmetic Method

Let's solve this problem using the arithmetic method. We'll create a model to represent the given information and use it to find the solution.

Let's assume the number of books on the first shelf is x. According to the given information, the second shelf has 3 more books than the first shelf, so the number of books on the second shelf is x + 3. Similarly, the third shelf has 4 more books than the second shelf, so the number of books on the third shelf is (x + 3) + 4.

According to the problem, the total number of books on all three shelves is 55. We can write this as an equation:

x + (x + 3) + ((x + 3) + 4) = 55

Now, let's solve this equation to find the value of x.

Algebraic Method

To solve the equation algebraically, we'll simplify and solve for x.

x + (x + 3) + ((x + 3) + 4) = 55

Simplifying the equation:

3x + 10 = 55

Subtracting 10 from both sides:

3x = 45

Dividing both sides by 3:

x = 15

So, the number of books on the first shelf is 15.

Using this value, we can find the number of books on the second and third shelves:

Number of books on the second shelf = x + 3 = 15 + 3 = 18

Number of books on the third shelf = (x + 3) + 4 = 18 + 4 = 22

Therefore, there are 15 books on the first shelf, 18 books on the second shelf, and 22 books on the third shelf.

Verification

To verify our solution, let's substitute the values we found back into the original equation and check if it holds true.

x + (x + 3) + ((x + 3) + 4) = 55

Substituting the values:

15 + (15 + 3) + ((15 + 3) + 4) = 55

Simplifying:

15 + 18 + 22 = 55

55 = 55

The equation holds true, which means our solution is correct.

Therefore, there are 15 books on the first shelf, 18 books on the second shelf, and 22 books on the third shelf.

Let me know if you need any further assistance!