Question

Є 9 порожніх великих коробок.у деякі з них поклали по 10 порожніх коробок середнього розміру,а у деякі коробки середнього розміру по 10 порожніх маленьких коробок.разом стало 109. скільки серед них було порожніх МАЛЕНЬКИХ коробок?

Answer 1

Нехай коробок середнього розміру було 10x (0<х<=9) , а маленьких 10y. Тоді  маємо

9+10x+10y=109

10x+10y=100

x+y=10

з останньої рівності і обмежень на х випливає, що число маленьких було або 10 (1*10), або 20 (2*10), або 30, або 40, або 50, або 60, або 70, або 80, або 90

Answer 2

Problem Analysis

We are given 9 large empty boxes. Some of these boxes contain 10 medium-sized empty boxes, while others contain 10 small empty boxes. In total, there are 109 boxes. We need to determine how many of these boxes are small empty boxes.

Solution

Let's assume that the number of large empty boxes is represented by L, the number of medium-sized empty boxes is represented by M, and the number of small empty boxes is represented by S.

From the given information, we can form the following equations:

1. L = 9 (There are 9 large empty boxes) 2. M + S = 109 (The total number of boxes is 109)

We also know that some of the large empty boxes contain 10 medium-sized empty boxes, and some of the medium-sized empty boxes contain 10 small empty boxes. This can be represented by the following equations:

3. M = 10L (The number of medium-sized empty boxes is 10 times the number of large empty boxes) 4. S = 10M (The number of small empty boxes is 10 times the number of medium-sized empty boxes)

Now, let's substitute the values from equations 1 and 3 into equation 4 to find the value of S:

S = 10M = 10(10L) = 100L

Substituting the value of L from equation 1 into the above equation, we get:

S = 100(9) = 900

Therefore, there are 900 small empty boxes among the given boxes.

Answer

There are 900 small empty boxes among the given boxes.