Question

2. В первом ящике было в 7 раз больше черешни, чем во втором. Когда из первого ящика взяли 24 кг черешни, а во второй добавили 18 кг, то в ящиках черешни стало поровну. Сколько килограммов черешни было в каждом ящике сначала?​

Answer 1

Пусть $x$ (кг) черешни было во 2 ящике сначала, тогда

$7x$ (кг) черешни было в 1 ящике сначала.

Уравнение.

$7x-24=x+18$

$7x-x=24+18$

$6x=42$

$x=42:6$

$x=7$ (кг) черешни было во 2 ящике сначала/

$7*7=49$  (кг) черешни было в 1 ящике сначала/

Ответ:  49кг;  7кг.

Answer 2

Problem Analysis

We are given two boxes of cherries, and it is stated that the first box contains 7 times more cherries than the second box. After taking 24 kg of cherries from the first box and adding 18 kg to the second box, the amount of cherries in both boxes becomes equal. We need to determine the initial amount of cherries in each box.

Solution

Let's assume the initial amount of cherries in the second box is x kg. According to the problem, the first box contains 7 times more cherries than the second box, so the initial amount of cherries in the first box is 7x kg.

After taking 24 kg of cherries from the first box, the amount of cherries remaining in the first box is (7x - 24) kg. Adding 18 kg to the second box, the amount of cherries in the second box becomes (x + 18) kg.

According to the problem, the amount of cherries in both boxes becomes equal after these operations. Therefore, we can set up the following equation:

7x - 24 = x + 18

Simplifying the equation:

6x = 42

Dividing both sides by 6:

x = 7

So, the initial amount of cherries in the second box was 7 kg, and the initial amount of cherries in the first box was 7 times more, which is 7 * 7 = 49 kg.

Therefore, there were initially 49 kg of cherries in the first box and 7 kg of cherries in the second box.