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Of the 350 people at a convention, [tex]80\%[/tex] had a regular pass, while the rest had a premium pass. There were 184 people who stayed for lunch, while the rest did not. Of the people who stayed for lunch, 52 had a premium pass.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Lunch & No Lunch & Total \\
\hline Regular Pass & & & \\
\hline Premium Pass & & & \\
\hline Total & & & \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
To solve this problem, let's break it down step-by-step to fill out the table:

1. Total People and Pass Types:
- There are a total of 350 people at the convention.
- [tex]\(80\%\)[/tex] of the people had a regular pass.
- The rest had a premium pass.

2. Calculate Number of People with Regular and Premium Passes:
- Regular Pass: [tex]\(80\% \text{ of } 350 = 0.8 \times 350 = 280\)[/tex] people.
- Premium Pass: [tex]\(20\% \text{ of } 350 = 0.2 \times 350 = 70\)[/tex] people.

3. People Who Stayed for Lunch:
- There were 184 people who stayed for lunch.
- Of these, 52 people had a premium pass.

4. Calculate Regular Pass Holders Who Stayed for Lunch:
- Total people who stayed for lunch: 184.
- Premium pass holders who stayed for lunch: 52.
- Regular pass holders who stayed for lunch: [tex]\(184 - 52 = 132\)[/tex] people.

5. Calculate People Who Did Not Stay for Lunch:
- Total people who did not stay for lunch: [tex]\(350 - 184 = 166\)[/tex] people.
- Premium pass holders who did not stay for lunch: [tex]\(70 - 52 = 18\)[/tex] people.
- Regular pass holders who did not stay for lunch: [tex]\(280 - 132 = 148\)[/tex] people.

Now we can fill in the table with these values:

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Lunch & No Lunch & Total \\ \hline Regular Pass & 132 & 148 & 280 \\ \hline Premium Pass & 52 & 18 & 70 \\ \hline Total & 184 & 166 & 350 \\ \hline \end{tabular} \][/tex]

So, the completed table is:

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Lunch & No Lunch & Total \\ \hline Regular Pass & 132 & 148 & 280 \\ \hline Premium Pass & 52 & 18 & 70 \\ \hline Total & 184 & 166 & 350 \\ \hline \end{tabular} \][/tex]

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