Berry Barter

Algebra Level 3

You have a strawberry farm next to your neighbor's blueberry farm. During the harvest season, you and your neighbor will exchange the goods in friendly barters as shown above: 1 strawberry for 2 blueberries, 3 strawberries for 5 blueberries, and 5 strawberries for 7 blueberries.

Over the last season, you gave your neighbor 36 strawberries and got 59 blueberries in return. If the number of trades for all three types of barters are all in prime numbers, how many times did you trade in total?

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