Chapter 12.3, Problem 22PPS

To determine

To find :Number of students are in Mrs. Rollins's class and in honors.

Answer to Problem 22PPS

  $94$

Explanation of Solution

Given information :

Probability, a student in honors, and attending Mrs. Rollin's class is $\frac{28}{51}$.

Probability, a student is not in Mrs. Rollin's class, he or she is not in honors is $\frac{33}{56}$.

  $165$ students that are neither in honors or Mrs. Rollin's class.

Calculation:

Let x number of students in not honors.

  $\begin{array}{l}\Rightarrow \frac{\text{33}}{\text{56}}x=165\\ \Rightarrow x=\frac{56\times 165}{33}=280,studentsnotinhonors\end{array}$

Total = $\text{(280 students – 165) = 115}$

Non-Honors student are in Mrs. Rollin's class.

Let y students are in Mrs. Rolling class,

  $\begin{array}{l}\Rightarrow \frac{\text{28}}{\text{51}}y=115\\ \Rightarrow y=\frac{115\times 51}{28}\approx 209,SuudentsinMrs.Rolling\text{'}sclass\end{array}$

Out of $209$ students, $115$ are not in honors therefore,

  $\text{209 – 115 = 94}$ students of honors are in Mrs. Rolling's class