Question

За 4 кг огірків і 5 кг помідорів заплатили 87 гр. Після подорожчання огірків в 3 рази і здешевлення помідорів в 3 рази за таку кількість заплатили 86 гр. Знайти початкову ціну.

Answer 1

Пусть Х - исходная цена огурцов, У - помидоров. Тогда верны равенства:
4*Х + 5*У = 87
и
4*(3*Х) + 5*(У/3) = 86
Получается система уравнений с двумя неизвестными. Выразим, например, из первого:
4*Х = 87 - 5*У
И подставим во второе:
3 * (87 - 5*У) + 5* (У/3) = 86
261 - 15*У + 5/3 *У = 86
175 = (15 - 5/3)*У = 40/3 У
У = 175*3 / 40 = 525 / 40 = 13,125
Отсюда:
Х = (87 - 5*У)/4 = (87 - 5*13,125)/4 = 21,375 / 4 = 5,34375
Ответы могут показаться некрасивыми, но, судя по проверке, они верны.

Answer 2

Problem Analysis

We are given that 4 kg of cucumbers and 5 kg of tomatoes were purchased for 87 UAH. After the price of cucumbers increased by 3 times and the price of tomatoes decreased by 3 times, the same quantity of cucumbers and tomatoes was purchased for 86 UAH. We need to find the initial price.

Solution

Let's assume the initial price of cucumbers is x UAH per kg and the initial price of tomatoes is y UAH per kg.

According to the given information, the total cost of 4 kg of cucumbers and 5 kg of tomatoes was 87 UAH. So, we can write the equation:

4x + 5y = 87 ---(1)

After the price of cucumbers increased by 3 times and the price of tomatoes decreased by 3 times, the same quantity of cucumbers and tomatoes was purchased for 86 UAH. So, we can write the second equation:

12x + (1/3)y = 86 ---(2)

To solve these equations, we can use the method of substitution or elimination. Let's use the method of elimination.

Multiplying equation (2) by 3, we get:

36x + y = 258 ---(3)

Now, we can subtract equation (1) from equation (3) to eliminate y:

(36x + y) - (4x + 5y) = 258 - 87

32x - 4y = 171 ---(4)

Simplifying equation (4), we get:

8x - y = 43 ---(5)

Now, we have a system of two equations:

4x + 5y = 87 ---(1) 8x - y = 43 ---(5)

We can solve this system of equations to find the values of x and y.

Let's solve the system of equations:

Multiplying equation (5) by 5, we get:

40x - 5y = 215 ---(6)

Adding equation (1) and equation (6), we can eliminate y:

(4x + 5y) + (40x - 5y) = 87 + 215

44x = 302

Dividing both sides by 44, we get:

x = 6.86

Substituting the value of x into equation (1), we can find the value of y:

4(6.86) + 5y = 87

27.44 + 5y = 87

5y = 87 - 27.44

5y = 59.56

Dividing both sides by 5, we get:

y = 11.912

Therefore, the initial price of cucumbers was approximately 6.86 UAH per kg and the initial price of tomatoes was approximately 11.912 UAH per kg.

Answer

The initial price of cucumbers was approximately 6.86 UAH per kg and the initial price of tomatoes was approximately 11.912 UAH per kg.