Thank you for visiting 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. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We are given that the café serves two drinks (tea and coffee) and three snacks (cookies, muffins, and scones), and the frequency table (with 500 total customers) is partially filled as follows:
[tex]$$
\begin{array}{|c|c|c|c|c|}
\hline
& \text{?} & \text{?} & \text{?} & \text{Total} \\
\hline
\text{Row 1} & 40 & 100 & 110 & 250 \\
\hline
\text{Row 2} & 120 & 80 & 50 & 250 \\
\hline
\text{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
Two key pieces of information are provided:
1. Approximately [tex]$24\%$[/tex] of the customers have a scone with their tea. Since [tex]$24\%$[/tex] of 500 is
[tex]$$
0.24\cdot 500 = 120,
$$[/tex]
the combination of tea and scone must account for 120 customers.
2. Approximately [tex]$36\%$[/tex] of the customers buy a muffin. Since [tex]$36\%$[/tex] of 500 is
[tex]$$
0.36\cdot 500 = 180,
$$[/tex]
the muffin column must have a total of 180 customers. Looking at the table's column totals, the only column with a total of 180 is the second column. Therefore, the second column represents muffins.
Now, let’s determine how to label the rows and the remaining snack columns.
Step 1. Identify the Tea and Scone Combination
Since tea with scone should be 120 customers, we search for where the number 120 appears in the table. In Row 2, the first column entry is 120. This suggests that if we assign Row 2 to tea, then the first column must represent scones (because then the tea and scone combination will be 120 customers, which matches the given condition).
Step 2. Label the Columns
- We already determined that the column with a total of 180 is for muffins. This is the second column.
- We have then identified that the first column is scones (to get the 120 tea-and-scone customers from Row 2).
- The remaining snack must be cookies. Therefore, the third column is cookies.
Step 3. Label the Rows
Since Row 2 has been designated for tea (to satisfy the tea scone condition), the other drink in the café is coffee, so Row 1 must be labeled coffee.
Final Assignments:
- Row 1: Coffee
- Row 2: Tea
- Column 1: Scone
- Column 2: Muffin
- Column 3: Cookie
Thus, the table with the completed labels becomes:
[tex]$$
\begin{array}{|c|c|c|c|c|}
\hline
& \text{scone} & \text{muffin} & \text{cookie} & \text{Total} \\
\hline
\text{coffee} & 40 & 100 & 110 & 250 \\
\hline
\text{tea} & 120 & 80 & 50 & 250 \\
\hline
\text{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
This step-by-step reasoning satisfies both conditions:
- The tea and scone cell has [tex]$120$[/tex] customers.
- The muffin column has a total of [tex]$180$[/tex] customers.
Therefore, the final answer is:
Row 1: coffee, Row 2: tea, Column 1: scone, Column 2: muffin, Column 3: cookie.
[tex]$$
\begin{array}{|c|c|c|c|c|}
\hline
& \text{?} & \text{?} & \text{?} & \text{Total} \\
\hline
\text{Row 1} & 40 & 100 & 110 & 250 \\
\hline
\text{Row 2} & 120 & 80 & 50 & 250 \\
\hline
\text{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
Two key pieces of information are provided:
1. Approximately [tex]$24\%$[/tex] of the customers have a scone with their tea. Since [tex]$24\%$[/tex] of 500 is
[tex]$$
0.24\cdot 500 = 120,
$$[/tex]
the combination of tea and scone must account for 120 customers.
2. Approximately [tex]$36\%$[/tex] of the customers buy a muffin. Since [tex]$36\%$[/tex] of 500 is
[tex]$$
0.36\cdot 500 = 180,
$$[/tex]
the muffin column must have a total of 180 customers. Looking at the table's column totals, the only column with a total of 180 is the second column. Therefore, the second column represents muffins.
Now, let’s determine how to label the rows and the remaining snack columns.
Step 1. Identify the Tea and Scone Combination
Since tea with scone should be 120 customers, we search for where the number 120 appears in the table. In Row 2, the first column entry is 120. This suggests that if we assign Row 2 to tea, then the first column must represent scones (because then the tea and scone combination will be 120 customers, which matches the given condition).
Step 2. Label the Columns
- We already determined that the column with a total of 180 is for muffins. This is the second column.
- We have then identified that the first column is scones (to get the 120 tea-and-scone customers from Row 2).
- The remaining snack must be cookies. Therefore, the third column is cookies.
Step 3. Label the Rows
Since Row 2 has been designated for tea (to satisfy the tea scone condition), the other drink in the café is coffee, so Row 1 must be labeled coffee.
Final Assignments:
- Row 1: Coffee
- Row 2: Tea
- Column 1: Scone
- Column 2: Muffin
- Column 3: Cookie
Thus, the table with the completed labels becomes:
[tex]$$
\begin{array}{|c|c|c|c|c|}
\hline
& \text{scone} & \text{muffin} & \text{cookie} & \text{Total} \\
\hline
\text{coffee} & 40 & 100 & 110 & 250 \\
\hline
\text{tea} & 120 & 80 & 50 & 250 \\
\hline
\text{Total} & 160 & 180 & 160 & 500 \\
\hline
\end{array}
$$[/tex]
This step-by-step reasoning satisfies both conditions:
- The tea and scone cell has [tex]$120$[/tex] customers.
- The muffin column has a total of [tex]$180$[/tex] customers.
Therefore, the final answer is:
Row 1: coffee, Row 2: tea, Column 1: scone, Column 2: muffin, Column 3: cookie.
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!
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Rewritten by : Jeany
