Thank you for visiting Drag each label to the correct location on the table A local café serves tea coffee cookies scones and muffins They recently gathered data about. 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 :
- Calculate the number of customers who had a scone with their tea: $0.24 \times 500 = 120$.
- Calculate the number of customers who bought a muffin: $0.36 \times 500 = 180$.
- Identify the 'Muffin' column as the one summing to 180.
- Deduce the remaining labels based on the intersection of 'Tea' and 'Scone' being 120, and the row and column totals.
- The final table labels are: Coffee, Tea, Scone, Muffin, Cookie.
### Explanation
1. Analyze the problem
We are given a frequency table representing a survey of customers at a café who purchased both a drink and a snack. The goal is to determine the correct labels for the rows and columns of the table, given that 24% of customers had a scone with their tea and 36% bought a muffin. The total number of customers surveyed is 500.
2. Calculate Tea and Scone intersection
First, calculate the number of customers who had a scone with their tea: $0.24 \times 500 = 120$. This means the intersection of the 'Tea' row and 'Scone' column (or vice versa) must be 120.
3. Calculate total Muffin sales
Next, calculate the number of customers who bought a muffin: $0.36 \times 500 = 180$. This means either a row or a column must sum to 180, and this row/column represents 'Muffins'.
4. Identify Muffin column
Looking at the table, we see that the second column sums to 180. Therefore, the second column represents 'Muffins'. Also, we see that the value 120 is in the second row and first column. If the second column is 'Muffins', then the first column cannot be 'Scones'. Therefore, the second row cannot be 'Tea'.
5. Identify Tea row and Scone column
Now, let's consider the row totals. The first row sums to 250, and the second row sums to 250. The column totals are 160, 180, and 160. We know that the 'Muffins' column sums to 180. We also know that the intersection of 'Tea' and 'Scone' is 120. Looking at the table, the only place where we can have 120 is the cell in the second row and the first column. This means that the first column must be 'Scone' and the second row must be 'Tea'.
6. Deduce remaining labels
If the first column is 'Scone' and the second column is 'Muffin', then the remaining column must be 'Cookie'. If the second row is 'Tea', then the remaining row must be 'Coffee'.
7. Final Table Labels
Therefore, the table should be labeled as follows:
| | Scone | Muffin | Cookie | Total |
|----------|-------|--------|--------|-------|
| Coffee | 40 | 100 | 110 | 250 |
| Tea | 120 | 80 | 50 | 250 |
| Total | 160 | 180 | 160 | 500 |
### Examples
Understanding customer preferences is crucial for businesses. By analyzing sales data like this, a café can optimize its menu, predict inventory needs, and create targeted promotions to increase sales. For example, they might offer a discount on tea and scones together, knowing that many customers enjoy this combination.
- Calculate the number of customers who bought a muffin: $0.36 \times 500 = 180$.
- Identify the 'Muffin' column as the one summing to 180.
- Deduce the remaining labels based on the intersection of 'Tea' and 'Scone' being 120, and the row and column totals.
- The final table labels are: Coffee, Tea, Scone, Muffin, Cookie.
### Explanation
1. Analyze the problem
We are given a frequency table representing a survey of customers at a café who purchased both a drink and a snack. The goal is to determine the correct labels for the rows and columns of the table, given that 24% of customers had a scone with their tea and 36% bought a muffin. The total number of customers surveyed is 500.
2. Calculate Tea and Scone intersection
First, calculate the number of customers who had a scone with their tea: $0.24 \times 500 = 120$. This means the intersection of the 'Tea' row and 'Scone' column (or vice versa) must be 120.
3. Calculate total Muffin sales
Next, calculate the number of customers who bought a muffin: $0.36 \times 500 = 180$. This means either a row or a column must sum to 180, and this row/column represents 'Muffins'.
4. Identify Muffin column
Looking at the table, we see that the second column sums to 180. Therefore, the second column represents 'Muffins'. Also, we see that the value 120 is in the second row and first column. If the second column is 'Muffins', then the first column cannot be 'Scones'. Therefore, the second row cannot be 'Tea'.
5. Identify Tea row and Scone column
Now, let's consider the row totals. The first row sums to 250, and the second row sums to 250. The column totals are 160, 180, and 160. We know that the 'Muffins' column sums to 180. We also know that the intersection of 'Tea' and 'Scone' is 120. Looking at the table, the only place where we can have 120 is the cell in the second row and the first column. This means that the first column must be 'Scone' and the second row must be 'Tea'.
6. Deduce remaining labels
If the first column is 'Scone' and the second column is 'Muffin', then the remaining column must be 'Cookie'. If the second row is 'Tea', then the remaining row must be 'Coffee'.
7. Final Table Labels
Therefore, the table should be labeled as follows:
| | Scone | Muffin | Cookie | Total |
|----------|-------|--------|--------|-------|
| Coffee | 40 | 100 | 110 | 250 |
| Tea | 120 | 80 | 50 | 250 |
| Total | 160 | 180 | 160 | 500 |
### Examples
Understanding customer preferences is crucial for businesses. By analyzing sales data like this, a café can optimize its menu, predict inventory needs, and create targeted promotions to increase sales. For example, they might offer a discount on tea and scones together, knowing that many customers enjoy this combination.
Thank you for reading the article Drag each label to the correct location on the table A local café serves tea coffee cookies scones and muffins They recently gathered data about. 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
