Question

Известно , что 4 кг огурцов и 3 кг помидоров стоили 34 грн.после того как огурцы подорожали на 50%, а помидоры подешевели на 20% , за 2кг огурцов и 5 кг помидоров заплатили 36грн . Найдите начальную стоимость 1кг огурцов и 1 кг помидоров

Answer 1

Пусть х (грн.) - цена 1 кг огурцов, у (грн.) - цена 1 кг помидоров.
1,5х - цена 1 кг огурцов после подорожания на 50%
0,8у - цена 1 кг помидоров после удешевления на 20%
Составим систему уравнений и решим её методом алгебраического сложения:
4х + 3у = 34
2 * 1,5х + 5 * 0,8у = 36
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4х + 3у = 34
3х + 4у = 36
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7х + 7у = 70
х + у = 10
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х = 10 - у     
Подставим значение х в первое уравнение системы
4(10 - у) + 3у = 34
40 - 4у + 3у = 34
40 - 34 = 4у - 3у
у = 6 (грн.) - первоначальная цена 1 кг помидоров
х = 10 - 6 = 4 (грн.) - первоначальная цена 1 кг огурцов
Ответ: 4 грн. - 1 кг огурцов; 6 грн. - 1 кг помидоров. 
Проверка: 4 * 4 + 3 * 6 = 16 + 18 = 34 грн.- первоначальная стоимость покупки
                  2 * 6 + 5 * 4,8 = 12 + 24 = 36 грн.- после

Answer 2

Calculating the Initial Cost of Cucumbers and Tomatoes

To find the initial cost of 1 kg of cucumbers and 1 kg of tomatoes, we can use the given information about the prices before and after the changes. Let's start by calculating the initial cost of 1 kg of cucumbers and 1 kg of tomatoes.

Given: - 4 kg of cucumbers + 3 kg of tomatoes = 34 UAH - After cucumbers increased by 50% and tomatoes decreased by 20%, 2 kg of cucumbers + 5 kg of tomatoes = 36 UAH

Let's denote the initial price of 1 kg of cucumbers as x and the initial price of 1 kg of tomatoes as y.

We can set up a system of equations based on the given information:

Equation 1: 4x + 3y = 34 (initial total cost of cucumbers and tomatoes) Equation 2: 2(1.5x) + 5(0.8y) = 36 (total cost after price changes)

Now, let's solve this system of equations to find the initial cost of 1 kg of cucumbers and 1 kg of tomatoes.

Solving the System of Equations

First, let's solve Equation 1 for y: 4x + 3y = 34 3y = 34 - 4x y = (34 - 4x)/3

Now, substitute the expression for y into Equation 2: 2(1.5x) + 5(0.8((34 - 4x)/3)) = 36 3x + 4(34 - 4x) = 36 3x + 136 - 16x = 36 -13x + 136 = 36 -13x = 36 - 136 -13x = -100 x = -100 / -13 x = 100 / 13 x = 7.69 (rounded to two decimal places)

Now that we have found the initial cost of 1 kg of cucumbers, we can find the initial cost of 1 kg of tomatoes using the expression for y: y = (34 - 4(7.69))/3 y = (34 - 30.76)/3 y = 3.24/3 y = 1.08 (rounded to two decimal places)

Conclusion

The initial cost of 1 kg of cucumbers was 7.69 UAH and the initial cost of 1 kg of tomatoes was 1.08 UAH.