10. 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?
Answer: A
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, first, we need to determine how many comic books they collectively own. Since Dave owns 44 comic books, we subtract this from the total of 128, leaving us with 84 comic books for Fred and Norman. Dividing this number by 2 gives us an average of 42 comic books each.
A) 42
This option is correct because it represents the average number of comic books owned by Fred and Norman. After calculating the total number of comic books they own (128 - 44 = 84) and dividing by the two individuals, the average is indeed 42.
B) 44
This option is incorrect as it suggests that Fred and Norman together own an average of 44 comic books each. If they owned that many, their total would be 44 x 2 = 88, which exceeds the 84 comic books available to them after accounting for Dave's share.
C) 46
This option is also incorrect as it implies that Fred and Norman own an average of 46 comic books each. If that were the case, their total would be 46 x 2 = 92, which again is more than the 84 comic books they have after deducting Dave's ownership.
D) 48
This option is incorrect as well, since it indicates that Fred and Norman would average 48 comic books each, leading to a total of 48 x 2 = 96. This total clearly surpasses the 84 comic books they actually share, making it impossible.
Conclusion
The correct answer is definitively 42, as this accurately reflects the average number of comic books owned by Fred and Norman based on the total they have after considering Dave's holdings. All other options fail because they propose averages that would result in totals exceeding the actual number of comic books available to Fred and Norman.