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Question 3 (Multiple Choice, Worth 2 points)

Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class. If the ratio of students who prefer free time at the beginning of class to students who prefer free time at the end of class is [tex]$\frac{12}{19}$[/tex], what does the ratio [tex]$\frac{12}{19}$[/tex] represent?

A. 19 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class.
B. 19 students prefer free time at the beginning of class, and 31 students prefer free time at the end of class.
C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
D. 31 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class.



Answer :

GinnyAnswer
To solve this problem, let's carefully analyze the given ratio and match it with the right statement from the provided options.

We are given a ratio of [tex]\(\frac{12}{19}\)[/tex], where the numerator represents students who prefer free time at the beginning of class, and the denominator represents students who prefer free time at the end of class.

So, according to the ratio:
- 12 represents the number of students who prefer free time at the beginning of class.
- 19 represents the number of students who prefer free time at the end of class.

Now, let's evaluate each option to find the correct one:
1. 19 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class:
- This suggests a ratio of [tex]\(\frac{19}{12}\)[/tex], which does not match the given [tex]\(\frac{12}{19}\)[/tex].

2. 19 students prefer free time at the beginning of class, and 31 students prefer free time at the end of class:
- This suggests a ratio of [tex]\(\frac{19}{31}\)[/tex], which does not match the given [tex]\(\frac{12}{19}\)[/tex].

3. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class:
- This precisely matches the given ratio of [tex]\(\frac{12}{19}\)[/tex].

4. 31 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class:
- This suggests a ratio of [tex]\(\frac{31}{12}\)[/tex], which does not match the given [tex]\(\frac{12}{19}\)[/tex].

After evaluating all the given options, the correct one is:
- 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

Therefore, the correct answer is:
- Option 3: 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

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