Question

В корзине было в два раза меньше мандаринов, чем в ящике. После того как из корзины переложили в ящик 10 мандаринов, в ящике их осталось в пять раз больше, чем в корзине. Сколько мандаринов было в корзине, и сколько в ящике ?

Answer 1

В корзине-два раза меньше
переложили-10ящ
всего-?

Answer 2

Ящик = Х, корзина = У.
Два неизвестных - два уравнения.
1) Х= 2У
2) Х+10 =5*(У-10) 
Подставим 1) в 2)
3) 2У+10 = 5У -50
Упрощаем выражение
4)  3У = 60
У = 20 шт - в корзине - ОТВЕТ
Х = 2У = 40 шт - в ящике - ОТВЕТ

Answer 3

Problem Analysis

We are given the information that there were twice as many mandarins in the box as there were in the basket. After transferring 10 mandarins from the basket to the box, there were five times as many mandarins in the box as there were in the basket. We need to determine the initial number of mandarins in the basket and the box.

Solution

Let's assume the initial number of mandarins in the basket is x. According to the given information, the number of mandarins in the box is twice that of the basket, so the initial number of mandarins in the box is 2x.

After transferring 10 mandarins from the basket to the box, the number of mandarins in the basket becomes x - 10, and the number of mandarins in the box becomes 2x + 10.

According to the second part of the information, there are five times as many mandarins in the box as there are in the basket. So, we can set up the equation:

2x + 10 = 5(x - 10)

Now, let's solve this equation to find the values of x and 2x.

Calculation

Expanding the equation:

2x + 10 = 5x - 50

Bringing like terms to one side:

2x - 5x = -50 - 10

Simplifying:

-3x = -60

Dividing both sides by -3:

x = 20

Substituting the value of x back into the equation to find 2x:

2x = 2 * 20 = 40

Answer

Therefore, there were 20 mandarins in the basket and 40 mandarins in the box initially.