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A local café serves tea, coffee, cookies, scones, and muffins. They recently gathered data about their customers who purchase both a drink and a snack. The given frequency table shows the results of the survey.

If approximately [tex]$24 \%$[/tex] of the customers surveyed have a scone with their tea and approximately [tex]$36 \%$[/tex] of the customers surveyed buy a muffin, complete the column and row headings for the given table.

Labels:
- Coffee
- Muffin
- Cookie
- Scone
- Tea

[tex]
\[
\begin{tabular}{|c|c|c|c|c|}
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & \text{Muffin} & \text{Cookie} & \text{Scone} & \text{Total} \\
\hline
\text{Tea} & 40 & 100 & 110 & 250 \\
\hline
\text{Coffee} & 120 & 80 & 50 & 250 \\
\hline
\text{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{tabular}
\]
[/tex]

Answer :

To solve the problem, let's determine the column and row headings of the frequency table based on the information given:

1. Identify the total number of customers:
The total number of customers surveyed is given as 500.

2. Calculate the number of tea and scone customers:
We know that approximately 24% of the customers have a scone with their tea. So, we calculate the number of these customers as follows:
[tex]\[
\text{Tea with scone customers} = 0.24 \times 500 = 120
\][/tex]

3. Calculate the total number of muffin buyers:
Approximately 36% of the customers buy a muffin. Therefore, the number of muffin customers is:
[tex]\[
\text{Muffin customers} = 0.36 \times 500 = 180
\][/tex]

4. Assign row and column labels to the table:
Start aligning the table based on the given percentages and totals.

- The first row total is 250, which indicates the total number of tea customers.
- The second row total is also 250, suggesting the total number of coffee customers.

5. Determine specific entries:
- Tea and muffin: If muffins total 180 and the given number of coffee and muffin customers is 80, the number of tea and muffin customers will be:
[tex]\[
\text{Tea with muffin customers} = 180 - 80 = 100
\][/tex]

- Coffee and scone: The total number of customers with scones is 160 (since it's from the total column for scone), and tea with scone is 120, so the number of coffee and scone customers will be:
[tex]\[
\text{Coffee with scone customers} = 160 - 120 = 40
\][/tex]

6. Complete the table:
Now we can complete the table using the derived values and already known ones.

```
\begin{tabular}{|c|c|c|c|c|}
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & Muffin & Cookie & Scone & Total \\
\hline
Tea & 40 & 100 & 110 & 250 \\
\hline
Coffee & 120 & 80 & 50 & 250 \\
\hline
Total & 160 & 180 & 160 & 500 \\
\hline
\end{tabular}
```

In this setup:
- Tea is paired with muffins (40), cookies (100), and scones (110).
- Coffee is paired with muffins (120), cookies (80), and scones (50).

This configuration ensures the row and column totals match the initial totals provided in the table.

Thank you for reading the article A local café serves tea coffee cookies scones and muffins They recently gathered data about their customers who purchase both a drink and a snack. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

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