3. Ophelia is paid $\$ 51$ for the first week of her part-time summer job. For each week after the first, she is paid $\$ 100$. How many weeks in total does she have to work for her average weekly pay to be $\$ 93$ ?
3. Solution 1
Suppose that Ophelia works for a total of $n$ weeks.
Then she earns $\$ 51$ for 1 week and $\$ 100$ a week for $(n-1)$ weeks.
Since her average weekly pay is $\$ 93$, then $\frac{51+(n-1) \times 100}{n}=93$.
Therefore,
$$
\begin{aligned}
51+100(n-1) & =93 n \\
51+100 n-100 & =93 n \\
100 n-49 & =93 n \\
100 n-93 n & =49 \\
7 n & =49 \\
n & =7
\end{aligned}
$$

Thus, Ophelia works for a total of 7 weeks.
Solution 2
We make a table that lists what Ophelia earns each week, the total that she has earned at the end of that week, and her average weekly pay so far:
\begin{tabular}{|c|c|c|c|}
\hline Week & Pay this week (\$) & Total pay so far (\$) & Average pay so far (\$) \\
\hline 1 & 51 & 51 & 51.00 \\
2 & 100 & 151 & $151 \div 2=75.50$ \\
3 & 100 & 251 & $251 \div 3 \approx 83.67$ \\
4 & 100 & 351 & $351 \div 4=87.75$ \\
5 & 100 & 451 & $451 \div 5=90.20$ \\
6 & 100 & 551 & $551 \div 6 \approx 91.83$ \\
7 & 100 & 651 & $651 \div 7=93.00$ \\
\hline
\end{tabular}

Therefore, Ophelia's average weekly pay is $\$ 93$ after she has worked for 7 weeks.
ANSWER: 7