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Fruit at a market

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At a market stall, $3$ kilograms of apples and $2$ kilograms of pears cost $16$ euros in total, while $5$ kilograms of apples cost $18$ euros more than $1$ kilogram of pears. Each fruit has a fixed price per kilogram. What is the price of $1$ kilogram of pears, in euros?

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Hint

Write one equation per condition and eliminate one of the prices.

Solution

With $x$ for the price of apples and $y$ for pears, the conditions read $3 x + 2 y = 16$ and $5 x - y = 18$ .
The second equation gives $y = 5 x - 18$ .
Substituting into the first gives $3 x + 10 x - 36 = 16$ , so $13 x = 52$ and $x = \frac{52}{13} = 4$ .
Then $y = 5 \times 4 - 18 = 2$ .

Answer: $2$

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