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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?

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Find conditional probabilities

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?

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. To express this situation mathematically, we can write the equation: $\newline$ $\frac{1}{3} \times p - 3 = 114$
Equation Setup: To find the equation that represents $p$ , we need to isolate $p$ on one side of the equation. First, we can add $3$ to both sides of the equation to get rid of the subtraction of $3$ from one-third of $p$ : $\frac{1}{3} \times p - 3 + 3 = 114 + 3$
Addition to Eliminate Subtraction: Simplifying both sides of the equation gives us: $\frac{1}{3} \times p = 117$
Simplify Equation: Now, to solve for $p$ , we need to multiply both sides of the equation by $3$ to cancel out the division by $3$ on the left side: $\newline$ $3 \times (\frac{1}{3} \times p) = 117 \times 3$
Isolate $p$ to Find Total Pages: This simplifies to: $p = 351$

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