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?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter6: Systems Of Linear Equations And Inequalities
Section6.6: Systems Of Inequalities
Problem 44PFA
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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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