Question

Решить задачу:В первом ящике было в 5раз больше груш, чем во втором. Когда из первого ящика взяли 16 груш, а во второй положили 12 груш, в ящиках груш стало поровну. Сколько груш было в каждом ящике сначала?

Answer 1

5х-16=х+12
4х=12+16=28
х=7

Answer 2

5x-16=x+12
5x-16+x-12=0
4x-28=0
4x=28
X=7

Answer 3

Problem Analysis

To solve this problem, we need to determine the number of pears in each box initially. We are given that the first box initially had 5 times more pears than the second box. After taking 16 pears from the first box and putting 12 pears into the second box, the number of pears in both boxes became equal.

Solution

Let's assume that the number of pears in the second box is x. According to the problem, the first box initially had 5 times more pears than the second box, so the number of pears in the first box is 5x.

After taking 16 pears from the first box, the number of pears in the first box becomes 5x - 16. After putting 12 pears into the second box, the number of pears in the second box becomes x + 12.

According to the problem, the number of pears in both boxes became equal. Therefore, we can set up the following equation:

5x - 16 = x + 12

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

5x - 16 = x + 12

Simplifying the equation:

5x - x = 12 + 16

4x = 28

Dividing both sides by 4:

x = 7

So, the second box initially had 7 pears. Since the first box initially had 5 times more pears than the second box, the first box initially had 5 * 7 = 35 pears.

Therefore, there were 35 pears in the first box and 7 pears in the second box initially.

Answer

There were 35 pears in the first box and 7 pears in the second box initially.