Danish read 15 pages of a book in a day. Wesley read 20 pages of the same book in a day. Danish started reading the book 3 days earlier than Wesley. How many days would Wesley need to read the book to be 20 pages ahead of Danish?
Danish read 15 pages of a book in a day. Wesley read 20 pages of the same book in a day. Danish started reading the book 3 days earlier than Wesley. How many days would Wesley need to read the book to be 20 pages ahead of Danish?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem 42:**
**Description:**
Danish read 15 pages of a book in a day. Wesley read 20 pages of the same book in a day. Danish started reading the book 3 days earlier than Wesley. How many days would Wesley need to read the book to be 20 pages ahead of Danish?
**Solution Strategy:**
To determine the number of days Wesley needs to read the book to be 20 pages ahead of Danish, we must establish a system of equations based on their reading rates and the initial conditions given.
Let \( d \) be the number of days Wesley reads the book.
### Steps to Solve:
1. Determine the number of pages Danish has read by the time Wesley starts:
- Danish reads for 3 days before Wesley, and his reading rate is 15 pages/day.
- Total pages read by Danish in 3 days: \( 15 \times 3 = 45 \) pages.
2. Express the total pages read by Danish and Wesley:
- Pages read by Danish after \( d \) days: \( 15(d + 3) \)
- Pages read by Wesley after \( d \) days: \( 20d \)
3. Set up the equation:
- We want Wesley to be 20 pages ahead of Danish.
- \( 20d = 15(d + 3) + 20 \)
4. Solve the equation for \( d \):
\[
20d = 15(d + 3) + 20
\]
\[
20d = 15d + 45 + 20
\]
\[
20d = 15d + 65
\]
\[
20d - 15d = 65
\]
\[
5d = 65
\]
\[
d = \frac{65}{5}
\]
\[
d = 13
\]
Wesley would need to read the book for 13 days to be 20 pages ahead of Danish.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F230199af-f664-4f93-821b-7cfa5784f333%2F826fb2a1-48e1-4354-b432-784561629299%2Fqucqfls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 42:**
**Description:**
Danish read 15 pages of a book in a day. Wesley read 20 pages of the same book in a day. Danish started reading the book 3 days earlier than Wesley. How many days would Wesley need to read the book to be 20 pages ahead of Danish?
**Solution Strategy:**
To determine the number of days Wesley needs to read the book to be 20 pages ahead of Danish, we must establish a system of equations based on their reading rates and the initial conditions given.
Let \( d \) be the number of days Wesley reads the book.
### Steps to Solve:
1. Determine the number of pages Danish has read by the time Wesley starts:
- Danish reads for 3 days before Wesley, and his reading rate is 15 pages/day.
- Total pages read by Danish in 3 days: \( 15 \times 3 = 45 \) pages.
2. Express the total pages read by Danish and Wesley:
- Pages read by Danish after \( d \) days: \( 15(d + 3) \)
- Pages read by Wesley after \( d \) days: \( 20d \)
3. Set up the equation:
- We want Wesley to be 20 pages ahead of Danish.
- \( 20d = 15(d + 3) + 20 \)
4. Solve the equation for \( d \):
\[
20d = 15(d + 3) + 20
\]
\[
20d = 15d + 45 + 20
\]
\[
20d = 15d + 65
\]
\[
20d - 15d = 65
\]
\[
5d = 65
\]
\[
d = \frac{65}{5}
\]
\[
d = 13
\]
Wesley would need to read the book for 13 days to be 20 pages ahead of Danish.
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