Question

Chandra and Bob, who each have a copy of the book, decide that they can save time by "team reading" the novel. In this scheme, Chandra will read from page $1$ to a certain page and Bob will read from the next page through page $760,$ finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?

$425$

$444$

$456$

$484$

$506$

Solution:

Let $x$ be the number of pages that Chandra will read. Then Bob will read $760 - x$ pages.

For them to read for the same amount of time, $\begin{align*} 30x &= 45(760 - x) \\ 30x &= 45 \cdot 760 - 45x \\ 75x &= 45 \cdot 760 \\ 5x &= 3 \cdot 760 \\ x &= 3 \cdot 152 \\ x &= 456. \end{align*}$

Thus, C is the correct answer.

2006 AMC 8 Problem 15

Solution:

Problem 15 in Other Years