Fruit seller/Price conditions/Orthogonal space/Exercise

A fruit seller sells apples, pears, and cherries. He cannot remember exactly his purchase prices, but he remembers that he has paid for ${}5$ kilograms of apples, the same as for ${}3$ kilograms of pears and one kilogram of cherries together. Moreover, naturally, the old fruit-seller-rule holds that the price of ${}3$ kilograms of apples equals the price of one kilogram of pears and one kilogram of cherries together. How does the orthogonal space for these price conditions look like? What is the price for one kilogram of apples if the price for one kilogram of cherries is ${}5$ Euro?

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