At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 6 are painted pink, 14 are painted blue, and 20 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 68 times, what are the minimum and maximum amounts of candy that could be handed out?
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Final Answer: The minimum amount of candy that could be handed out is \(\boxed{68}\) and the maximum amount of candy that could be handed out is \(\boxed{94}\).
Step 1 ：At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 6 are painted pink, 14 are painted blue, and 20 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 68 times, what are the minimum and maximum amounts of candy that could be handed out?
Step 2 ：The minimum amount of candy that could be handed out would be if the player selected a purple duck every time, as this gives the least amount of candy. So, the minimum candy would be \(68 \times 1 = 68\).
Step 3 ：The maximum amount of candy that could be handed out would be if the player selected a pink duck every time, as this gives the most amount of candy. However, since there are only 6 pink ducks and the game is played 68 times, the player can only select a pink duck 6 times. After that, they would have to select a blue duck, as this gives the next highest amount of candy. But since there are only 14 blue ducks, they can only select a blue duck 14 times. After that, they would have to select a purple duck for the remaining 48 times.
Step 4 ：So, the maximum candy would be \(6 \times 3 + 14 \times 2 + 48 \times 1 = 94\).
Step 5 ：Final Answer: The minimum amount of candy that could be handed out is \(\boxed{68}\) and the maximum amount of candy that could be handed out is \(\boxed{94}\).
