In Mr. Murrow's classroom, every student wants to participate the most. For every $3$ times Rebecca raises her hand, Tahmid raises his hand $4$ times. For every $2$ times John raises his hand, Danna raises her hand $3$ times. If John raises his hand $2$ times every time Tahmid raises his hand, who participates the most in class? $\newline$ A. Danna $\newline$ B. John $\newline$ C. Rebecca $\newline$ D. Tahmid

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Q. In Mr. Murrow's classroom, every student wants to participate the most. For every

3

times Rebecca raises her hand, Tahmid raises his hand

4

times. For every

2

times John raises his hand, Danna raises her hand

3

times. If John raises his hand

2

times every time Tahmid raises his hand, who participates the most in class?

\newline

A. Danna

\newline

B. John

\newline

C. Rebecca

\newline

D. Tahmid

Establish Baseline: Let's find out how often each student raises their hand in terms of a common baseline. We'll use Tahmid's participation as the baseline since everyone else's participation is compared to his.
Calculate Rebecca's Participation: First, we know that for every $3$ times Rebecca raises her hand, Tahmid raises his hand $4$ times. So, if we let the number of times Tahmid raises his hand be $T$ , then Rebecca raises her hand $(\frac{3}{4})T$ times.
Calculate John's Participation: Next, John raises his hand $2$ times for every time Tahmid raises his hand. So John raises his hand $2T$ times.
Calculate Danna's Participation: Danna raises her hand $3$ times for every $2$ times John raises his hand. Since John raises his hand $2T$ times, Danna raises her hand $(\frac{3}{2}) \times 2T = 3T$ times.
Compare Participation Levels: Now we compare the number of times each student raises their hand: Rebecca raises her hand $(\frac{3}{4})T$ times, John raises his hand $2T$ times, Danna raises her hand $3T$ times, and Tahmid raises his hand $T$ times.
Identify Most Active Participant: Since $T$ is the same for all students, we can compare the coefficients: Rebecca has $\frac{3}{4}$ , John has $2$ , Danna has $3$ , and Tahmid has $1$ . The largest coefficient is $3$ , which belongs to Danna.
Identify Most Active Participant: Since $T$ is the same for all students, we can compare the coefficients: Rebecca has $\frac{3}{4}$ , John has $2$ , Danna has $3$ , and Tahmid has $1$ . The largest coefficient is $3$ , which belongs to Danna.Therefore, Danna participates the most in class.