Question

Решите задачи с помощью уравнений. В мешке было в 4 раза огурцов больше, чем в корзине. После того, как из мешка достали 20кг, а в корзину добавили 30кг, то в мешке стало в 2 раза больше огурцов, чем в корзине. Сколько килограммов огурцов было в мешке первоначально?

Answer 1

Допустим в корзине было х кг огурцов,значит в мешке было 4х кг.
итак исходя из условия задачи получаем уравнение : 2(х+30)=4х-20
                                                                                    2х+60=4х-20
                                                                                    2х=80
                                                                                    х=40кг
                                                                                    4х=160кг
Ответ:в мешке было 160 кг огурцов.

Answer 2

Problem Solving with Equations: Number of Cucumbers in the Bag

To solve this problem, let's assign variables to the unknown quantities. Let's say the number of cucumbers in the bag initially is represented by 'x', and the number of cucumbers in the basket initially is represented by 'y'.

According to the problem statement, we have the following information:

1. The number of cucumbers in the bag is 4 times more than the number of cucumbers in the basket: x = 4y.

2. After taking out 20 kg from the bag and adding 30 kg to the basket, the number of cucumbers in the bag becomes twice the number of cucumbers in the basket: (x - 20) = 2(y + 30).

We can now solve these two equations simultaneously to find the values of 'x' and 'y'.

Let's start by solving the first equation for 'x' in terms of 'y':

x = 4y ---(Equation 1)

Now, substitute the value of 'x' from Equation 1 into Equation 2:

(4y - 20) = 2(y + 30) ---(Equation 2)

Simplifying Equation 2:

4y - 20 = 2y + 60

Subtracting 2y from both sides:

2y - 20 = 60

Adding 20 to both sides:

2y = 80

Dividing both sides by 2:

y = 40

Now that we have the value of 'y', we can substitute it back into Equation 1 to find the value of 'x':

x = 4y x = 4 * 40 x = 160

Therefore, the initial number of cucumbers in the bag was 160 kilograms.

Please let me know if you need any further assistance!