12. Alexia, Bob, and Comelia recorded the number of pages of books they read last month. Alexia read 135 pages, Bob read 26 pages less than Alexia, and Comelia read 3 and one-half × more pages than Alexia and Bob combined. Which of the following represents the total number of pages that Alexia, Bob, and Comelia read last month?
Answer: C
4.5[2(135) - 26]
The total number of pages that Alexia, Bob, and Comelia read last month can be accurately represented by the expression 4.5[2(135) - 26]. This expression accounts for the number of pages each person read, factoring in the relationship between their readings.
A) 3.5(135 + 26)
This option is incorrect because it does not accurately represent the total number of pages read by Comelia. It suggests that Comelia read 3.5 times the sum of Alexia's and Bob's pages, which is not consistent with the information provided.
B) 3.5[2(135) - 26]
While this option correctly multiplies by 3.5, it incorrectly uses the expression 2(135) - 26, which does not accurately reflect the sum of Alexia's and Bob's pages. This option fails to incorporate the correct relationship as described in the question context.
C) 4.5[2(135) - 26]
This option is correct as it accurately reflects that Comelia read 3.5 times the total of Alexia's and Bob's pages combined. The expression 2(135) - 26 effectively calculates the total pages read by Alexia and Bob, and multiplying by 4.5 captures the total read by Comelia as well.
D) 4.5[2(135) + 26]
This option is incorrect because it adds 26 instead of subtracting it from the total of Alexia's pages. This miscalculation does not reflect Bob's reading accurately and therefore fails to provide the correct total.
Conclusion
The correct answer, C) 4.5[2(135) - 26], represents the total number of pages read by all three individuals accurately, taking into account the specified relationships between their readings. The other options either miscalculate the contributions of Alexia and Bob or misinterpret the multiplication factor for Comelia, rendering them incorrect.