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John read the first 114 pages of a novel, which was 3 pages less than
(1)/(3) of the novel. If
p is the total number of pages in the novel, which of the following equations best describes the situation?
Choose 1 answer:
(A)
(1)/(3)p-3=114
(B)
(1)/(3)p+3=114
(C)
3p-3=114
(D)
3p+3=114

John read the first $114$ pages of a novel, which was $3$ pages less than $\frac{1}{3}$ of the novel. If $p$ is the total number of pages in the novel, which of the following equations best describes the situation? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{3} p-3=114$ $\newline$ (B) $\frac{1}{3} p+3=114$ $\newline$ (C) $3 p-3=114$ $\newline$ (D) $3 p+3=114$

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Write two-variable inequalities: word problems

Full solution

Q. John read the first

114

pages of a novel, which was

3

pages less than

\frac{1}{3}

of the novel. If

p

is the total number of pages in the novel, which of the following equations best describes the situation?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{3} p-3=114

\newline

(B)

\frac{1}{3} p+3=114

\newline

(C)

3 p-3=114

\newline

(D)

3 p+3=114

Define Total Pages: Let's denote the total number of pages in the novel as $p$ . According to the problem, John read $114$ pages, which is $3$ pages less than one-third of the total number of pages. This can be expressed as one-third of the total number of pages minus $3$ equals $114$ pages. Mathematically, this is written as $(\frac{1}{3})p - 3 = 114$ .
Equation Setup: To check if this equation makes sense, we can add $3$ to both sides of the equation to isolate the term involving $p$ . This gives us $(\frac{1}{3})p = 114 + 3$ . Simplifying the right side gives us $(\frac{1}{3})p = 117$ . This means that one-third of the total number of pages is $117$ , which seems reasonable and does not indicate a math error.
Solve for Total Pages: Now, we can multiply both sides of the equation by $3$ to solve for $p$ . This gives us $p = 117 \times 3$ . Calculating this, we get $p = 351$ . This means the total number of pages in the novel would be $351$ , which is consistent with the information given in the problem.

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