College

John read the first 114 pages of a novel, which was 3 pages less than [tex]\frac{1}{3}[/tex] of the novel. If [tex]p[/tex] is the total number of pages in the novel, which of the following equations best describes the situation?

A. [tex]\frac{1}{3}p - 3 = 114[/tex]
B. [tex]3p - 3 = 114[/tex]
C. [tex]\frac{1}{3}p + 3 = 114[/tex]
D. [tex]p - 3 = 114[/tex]

Answer :

To solve the problem, we need to set up an equation to find the total number of pages, [tex]\( p \)[/tex], in the novel based on the information given.

1. Understanding the Problem:
- John read 114 pages, which is 3 pages less than one-third of the entire novel.

2. Setting Up the Equation:
- We know that 114 pages are 3 pages less than [tex]\(\frac{1}{3}\)[/tex] of the total pages. This can be expressed in equation form as:
[tex]\[
114 = \frac{1}{3}p - 3
\][/tex]

3. Solving the Equation:
- First, add 3 to both sides of the equation to eliminate the '-3':
[tex]\[
114 + 3 = \frac{1}{3}p
\][/tex]
[tex]\[
117 = \frac{1}{3}p
\][/tex]
- Next, solve for [tex]\( p \)[/tex] by multiplying both sides by 3 to cancel the fraction:
[tex]\[
p = 117 \times 3
\][/tex]
[tex]\[
p = 351
\][/tex]

Thus, the equation [tex]\( 117 = \frac{1}{3}p \)[/tex] best describes the situation, and the total number of pages in the novel is 351.