Question

В одном ящике было в 7 раз больше апельсинов.чем в другом. Когда из первого ящика взяли 38 апельсинов. а из другого - 14 . то во втором осталось на 78 апельсинов меньше. чем в первом . Сколько апельсинов было в каждом ящике сначала?

Answer 1

Пусть во втором ящике было х апельсинов, то в первом 7х.
7х-38=х-14+78
7х-38=х+64
7х-х=64+38
6х=102
х=102:6
х=17
итак во втором ящике было 17 апельсинов, а в первом 17*7=119 апельсинов
Ответ: 119 апельсинов, 17 апельсинов.

Answer 2

Problem Analysis

We are given two boxes of oranges, and the number of oranges in one box is 7 times greater than the number of oranges in the other box. After taking 38 oranges from the first box and 14 oranges from the second box, there are 78 fewer oranges in the second box than in the first box. We need to determine the initial number of oranges in each box.

Solution

Let's assume the number of oranges in the first box is x and the number of oranges in the second box is y.

According to the given information: 1. The number of oranges in the first box is 7 times greater than the number of oranges in the second box: x = 7y. 2. After taking 38 oranges from the first box and 14 oranges from the second box, there are 78 fewer oranges in the second box than in the first box: y - 14 = x - 38 - 78.

To solve this system of equations, we'll substitute the value of x from the first equation into the second equation.

Substituting x = 7y into the second equation: y - 14 = 7y - 38 - 78

Simplifying the equation: y - 14 = 7y - 116

Bringing the variables to one side and the constants to the other side: -6y = -102

Dividing both sides by -6: y = 17

Substituting the value of y back into the first equation to find x: x = 7 * 17 = 119

Therefore, there were initially 119 oranges in the first box and 17 oranges in the second box.

Answer

There were initially 119 oranges in the first box and 17 oranges in the second box.