Fred, Norman, and Dave own a total of 128 comic books. If Dave owns 44 of them, what is the average (arithmetic mean) number of comic books owned by Fred and Norman?
The average number of comic books owned by Fred and Norman is 42.
To find the average number of comic books owned by Fred and Norman, we first subtract the number of comic books Dave owns from the total. With Dave owning 44 comic books, Fred and Norman together own 128 - 44 = 84 comic books. Dividing this total by 2 gives us an average of 42 comic books for each.
This choice is correct. By calculating the total owned by Fred and Norman (84 comic books) and dividing that by the two of them, we arrive at an average of 84 / 2 = 42 comic books each.
This choice incorrectly assumes that Fred and Norman together own more comic books than they actually do. Since Dave owns 44 comics, the remaining 84 comics owned by Fred and Norman, when divided, result in a lower average of 42.
Choosing 46 suggests that Fred and Norman together own 92 comic books, which is incorrect. The total they own is 84, and dividing this by two does not yield 46, indicating a miscalculation.
This option implies that Fred and Norman collectively possess 96 comic books, which exceeds the actual total of 84. Thus, dividing their comic book total by two cannot lead to an average of 48.
The arithmetic mean of comic books owned by Fred and Norman is accurately calculated as 42. By subtracting Dave's count from the total and dividing the remainder by two, we confirm that Fred and Norman's combined ownership results in an average of 42 comic books each. All other options misinterpret the total shared ownership, demonstrating the importance of accurate arithmetic in problem-solving.
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