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17 Apr 2025, 06:06
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Total: $220
First: $110
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
86% (01:46) correct
14%
(01:42)
wrong
based on 322
sessions
History
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In a certain raffle, the tickets that are purchased by participants are placed in a bin from which 3 will be drawn at random. The purchaser of the first ticket drawn will be awarded 50% of the total amount of money collected from ticket purchases. The purchasers of the second and third tickets drawn will be awarded equal shares of the remaining amount. The total of the amounts awarded will be the same as the total amount collected from ticket purchases, and all amounts awarded will be whole dollar amounts.
Select for Total and for First values that are jointly consistent with the information provided and could be the total amount collected from ticket sales and the amount awarded to the holder of the first ticket drawn.
Make only two selections in each column.
Select for Total and for First values that are jointly consistent with the information provided and could be the total amount collected from ticket sales and the amount awarded to the holder of the first ticket drawn.
Make only two selections in each column.
| Total | First | |
| $55 | ||
| $110 | ||
| $165 | ||
| $220 | ||
| $230 |
ShowHide Answer
Official Answer
Total: $220
First: $110
17 Apr 2025, 08:51
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Quote:
Let x = total amount of money collected
Purchaser of first ticket gets = 50% of x => 0.5x
Quote:
Remaining amount = x - 0.5x = 0.5x
Now we're given that this remaining amount will be divided equally amongst the second and third tickets so each will get 0.5x/2 or 0.25x
Quote:
Total amount was x, we're given that x will be whole dollar amounts => x needs to be an integer
Also, all amounts have to be dollar amounts so 0.25x and 0.5x both need to be integers
So we can now start from the first column.
If x = $55, 0.5x will not be an integer => Eliminate
If x = $110, 0.5x = $55, but 0.25x = 55/2, not an integer => Eliminate
If x = $165, 0.5x will not be an integer => Eliminate
If x = $220, 0.5x = $110 and 0.25x = $55, all amounts are integers, so the total is $220. First is the purchaser of the first ticket, which is 0.5x => $110.
Hence first column (value of total) is $220, and the second column (value of first) is $110.
