To fill in the two-way table based on the provided information, let's break down the given data:
Given:
- 7th graders attending on Friday: 24
- 8th graders attending on Saturday: 35
- Total attendance on Friday: 52
To find how many 8th graders were present on Friday and how many 7th graders were present on Saturday, we can lay out the information as follows:
Table:
| | Friday | Saturday | Totals | |-----------|--------|----------|--------| | 7th Graders | 24 | ? | ? | | 8th Graders | ? | 35 | ? | | Totals | 52 | ? | ? |
Step 1: Finding 7th Graders on Saturday We know the total number of attendees on Friday is 52. We have 24 7th graders, so we can find the number of 8th graders on Friday:
- Total on Friday = 7th Graders on Friday + 8th Graders on Friday
- 52 = 24 + 8th Graders on Friday
- 8th Graders on Friday = 52 - 24 = 28
Step 2: Finding Total Attendance for Saturday Let's assume the total number of students on Saturday is the same as on Friday; we can denote the total on Saturday as \( x \).
The total attendance across both days:
- Total Attendance = Total on Friday + Total on Saturday
- To find Saturday's total, we can set up the equation:
- Total on Saturday = 7th Graders on Saturday + 8th Graders on Saturday
- Therefore, we have the complete row for Friday, and we can express Saturday in terms of 7th Graders on Saturday, which we have left as "?".
Now substituting everything we know into the table:
| | Friday | Saturday | Totals | |-----------|--------|----------|--------| | 7th Graders | 24 | ? | ? | | 8th Graders | 28 | 35 | ? | | Totals | 52 | ? | ? |
Step 3: Completing the table: We need to calculate the total attendance by summing the values in each row.
The total number of 8th graders is the sum of 8th graders who were present on Friday and Saturday:
- Total 8th Graders = 28 (Friday) + 35 (Saturday) = 63
So the completed table should look like:
| | Friday | Saturday | Totals | |-----------|--------|----------|--------| | 7th Graders | 24 | ? | ? | | 8th Graders | 28 | 35 | 63 | | Totals | 52 | ? | ? |
Final Answer: The total number of 8th graders is 63.