To construct a two-way table and find the total number of 8th graders, we can fill in the information given in the text.
Two-Way Table:
| | Friday | Saturday | Totals | |------------|--------|----------|--------| | 7th graders| 24 | ? | ? | | 8th graders| 35 | ? | ? | | Totals | 52 | ? | ? |
From the table, we know the following:
- Total number of students attending Friday = 52
- Total number of 7th graders on Friday = 24
- Total number of 8th graders on Friday = 35
First, we find the total number of students on Saturday. To find it, we need to subtract the attendance on Friday from the total attendance, which consists of both 7th and 8th graders.
Given that 7th graders on Friday are 24 and 8th graders on Friday are 35, we can determine the Saturday attendance.
Calculate Saturday Total: Total attendance = Total 7th graders + Total 8th graders Total 7th graders = 24 (Friday) Total 8th graders = 35 + (unknown number of 8th graders on Saturday)
We know the total attendance for both days combined, so calculate the Saturday total: Total attendance = Total for Friday + Total for Saturday 52 (Friday attendance)
Since 35 are 8th graders who we assume are present on Friday, we can calculate the possible number attending on Saturday.
Let’s denote the number of 7th graders attending on Saturday as “x” and the number of 8th graders as “y”.
The Saturday table will also require us to find the total students who attended over Friday.
Since the total for Friday is 52, we can set the equation: \[ x + y = \text{Saturday Total} \] We don't know the Saturday total yet.
Also, for the totals: \[ 24 + x = \text{Total 7th Graders} \] \[ 35 + y = \text{Total 8th Graders} \]
Thus, Total attendance from Friday = 52
From Friday’s numbers, we have:
- 24 (7th) + 35 (8th) = 59 total attending (combined for Friday)
Assuming it’s complete, let’s check Saturday attendance by assumption: Let’s say we need to test responses for totals, repeating: We can try different responses:
- 59 (Total 8th graders)
- 28
- 63 (incorrects)
- 35 (incorrects)
From the calculations, it's clear straightforwardly the total of **59, the entire number of 7th and 8th included aligns to accommodate variations. Clearly a tally of 24 (7th graders), 35 (8th graders) means 59 (eighth peace). The only valid possibility here is 59 confirmed as designated.
So, the total number of 8th graders is 59.