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\begin{tabular}{lcc}
& Website A & Website B \\
\hline Number of writers & 5 & 11 \\
Number of posts posted & 110 & 200 \\
Average number of words of post & 100 & 170 \\
Average likes per post & 3500 & 3500 \\
Average comments per post & 500 & 450 \\
Number of new subscribers & 9000 & 20,000 \\
Revenue & [tex]$\$[/tex] 30,000[tex]$ & $[/tex]\[tex]$ 75,000$[/tex] \\
Expenses & [tex]$\$[/tex] 20,000[tex]$ & $[/tex]\[tex]$ 47,000$[/tex] \\
\hline Profit (Revenue-Expenses) & [tex]$\$[/tex] 10,000[tex]$ & $[/tex]\[tex]$ 28,000$[/tex] \\
\hline
\end{tabular}

Charlotte wants to know which website has more user engagement per dollar of expense.

1) Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options.



Answer :

GinnyAnswer
To determine which website has more user engagement per a single dollar expense, we need to consider two different definitions of user engagement per expense.

1. Total User Engagement per Dollar Expense:

This definition measures how much engagement (likes, comments, and subscribers combined) each website generates for each dollar spent. We will calculate this as follows:

[tex]\[ \text{Engagement per Dollar} = \frac{\text{Total Engagement (Likes + Comments + Subscribers)}}{\text{Expenses}} \][/tex]

Let's apply this to both websites:

- Website A:
[tex]\[ \text{Total Engagement} = \text{Likes (3500)} + \text{Comments (500)} + \text{Subscribers (9000)} = 13000 \][/tex]

[tex]\[ \text{Engagement per Dollar for Website A} = \frac{13000}{20000} \approx 0.65 \][/tex]

- Website B:
[tex]\[ \text{Total Engagement} = \text{Likes (3500)} + \text{Comments (450)} + \text{Subscribers (20000)} = 23950 \][/tex]

[tex]\[ \text{Engagement per Dollar for Website B} = \frac{23950}{47000} \approx 0.5096 \][/tex]

Thus, for total user engagement per dollar:

- Website A has an engagement of approximately 0.65 per dollar.
- Website B has an engagement of approximately 0.5096 per dollar.

2. Total User Engagement per Post per Dollar Expense:

This definition measures how much engagement each post generates for each dollar spent on the website. We will calculate this as follows:

[tex]\[ \text{Engagement per Post per Dollar} = \frac{\text{Total Engagement}}{\text{Number of Posts} \times \text{Expenses}} \][/tex]

Let's apply this to both websites:

- Website A:
[tex]\[ \text{Engagement per Post per Dollar for Website A} = \frac{13000}{110 \times 20000} \approx 0.005909 \][/tex]

- Website B:
[tex]\[ \text{Engagement per Post per Dollar for Website B} = \frac{23950}{200 \times 47000} \approx 0.002548 \][/tex]

Thus, for total user engagement per post per dollar:

- Website A has an engagement of approximately 0.005909 per post per dollar.
- Website B has an engagement of approximately 0.002548 per post per dollar.

In summary, the two definitions of user engagement per dollar expense that Charlotte should consider are:

1. Total User Engagement per Dollar Expense
2. Total User Engagement per Post per Dollar Expense

Based on these calculations, Website A performs better in both metrics compared to Website B.

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