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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8.
After the shipwreck, Captain Grant and two of his deck hands - Angus and Blaine - are on the island Tabor and are now trading goods with one another. Captain Grant exchanges 6 albatross eggs and 18 bananas for 30 oysters from Blaine. Then, Blaine exchanges 10 oysters and 10 of the bananas for 6 albatross eggs from Angus. How many bananas is an egg worth?
If 6 eggs are worth 10 oysters and 10 bananas, then Captain Grant has exchanged the equivalent of 10 oysters and 28 bananas for 30 oysters. Therefore, 28 bananas are worth 20 oysters. Then, 10 oysters are worth 14 bananas and Blaine paid the equivalent of 24 bananas for 6 more eggs. That's 4 bananas for 1 egg!
Algebraically, we can set up the system:
Multiplying the second equation by 3:
and substituting for the 6 eggs in the first equation:
we get 4 bananas to an egg.