Question

Позор мне. Не могу решить. За 2 кг яблок и 3 кг груш заплатили 31 грн. Сколько стоит 1 кг яблок и 1кг груш, если груши на 2 грн дороже.

Answer 1

5 грн стоит 1 кг яблок

Answer 2

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To answer your question, let me translate it first using Google Translate:

Answer in detail. Shame on me. I can't decide. For 2 kg of apples and 3 kg of pears, they paid 31 UAH. How much does 1 kg of apples and 1 kg of pears cost, if pears are 2 UAH more expensive.

This is a system of linear equations. Let x be the price of 1 kg of apples and y be the price of 1 kg of pears. Then we have:

$$ \begin{cases} 2x + 3y = 31 \\ y = x + 2 \end{cases} $$

To solve this system, we can substitute y with x + 2 in the first equation and get:

$$ 2x + 3(x + 2) = 31 $$

Simplifying and solving for x, we get:

$$ 5x + 6 = 31 \\ 5x = 25 \\ x = 5 $$

Therefore, the price of 1 kg of apples is 5 UAH. To find the price of 1 kg of pears, we can use the second equation and get:

$$ y = x + 2 \\ y = 5 + 2 \\ y = 7 $$

Therefore, the price of 1 kg of pears is 7 UAH.

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