A buyer purchases ducks for $4 each and geese for $7 each, spending precisely $53. If the buyer obtained more ducks than geese and bought at least one of each, what was the total number of birds purchased?
11 birds
We solve 4d + 7g = 53 for positive integers d and g with d > g. Testing values: if g = 3, then 4d + 21 = 53, giving 4d = 32, so d = 8. Here, 8 ducks > 3 geese, giving 8 + 3 = 11 birds. (The other integer solution, g = 7 and d = 1, fails the condition d > g).
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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