Question

Chris read 312 pages of a book at first. He read the remaining pages in 20 days, with the same number of pages each day. During these 20 days,he read one-twelveth(1over12) of the book in 6days. How many pages of the book did he read in those 6 days?

Answer 1

Let's denote the total number of pages in the book as \( P \).

Chris read one-twelfth of the book in 6 days, meaning he read:

\[
\frac{P}{12}
\]

in 6 days.

To find out how many pages he read each day during these 6 days, we calculate:

\[
\text{Pages read per day} = \frac{\frac{P}{12}}{6} = \frac{P}{72}.
\]

Next, in the 20 days, he read the remaining pages after the first 312 pages. The remaining pages he read in 20 days is given by:

\[
\text{Remaining pages} = P - 312.
\]

Since he read the same number of pages each day over 20 days, we can express this as:

\[
\text{Pages read per day over 20 days} = \frac{P - 312}{20}.
\]

Now we know the number of pages read per day during the 20 days must be equal to the number of pages read per day during the first 6 days:

\[
\frac{P - 312}{20} = \frac{P}{72}.
\]

Next, we solve this equation. We can cross-multiply:

\[
72(P - 312) = 20P.
\]

Expanding both sides gives:

\[
72P - 22464 = 20P.
\]

Now, we can rearrange this to isolate \( P \):

\[
72P - 20P = 22464,
\]
\[
52P = 22464.
\]

Now, dividing both sides by 52:

\[
P = \frac{22464}{52} = 432.
\]

Now that we have the total number of pages in the book \( P \), we can find how many pages Chris read in those 6 days:

\[
\text{Pages read in 6 days} = \frac{P}{12} = \frac{432}{12} = 36.
\]

Therefore, the number of pages Chris read in those 6 days is:

\[
\boxed{36}.
\]