long question-sorry
I'm a teacher with study hall 1st period & 3 games in my closet-polled the students to see who would play which game. (The problem on my paper gives names, but I'm just giving numbers.) 5 kids said they would play all 3 games. 5 others said they wouldn't play any games. 3 said they would play checkers & backgammon- 2 said they'd play backgammon & chess-1 would play chess & checkers. This gave the teacher 21 students who would play backgammon or chess, 24 who would play checkers or chess, & 26 who would play checkers or backgammon. How many students wanted to play only backgammon?Only checkers?Only chess? How many were in the study hall?
This is study hall? Times have changed.
yeah, they're no longer allowed to sleep - actually, it must be a non-tenured teacher trying to keep the job- either way, the teacher's just trying to survive - can you help?
If you have names, put them on a spreadsheet, names down, games across in columns.
You can answer each question by counting.
I'd use a venn diagram. Simple, yet effective.
i don't have enough names to make those numbers work, but thanks
To solve this problem, let's break it down step by step:
Step 1: Analyze the information given in the problem
- 5 students would play all 3 games.
- 5 students wouldn't play any games.
- 3 students would play checkers and backgammon.
- 2 students would play backgammon and chess.
- 1 student would play chess and checkers.
- The teacher had a total of 21 students who would play backgammon or chess.
- The teacher had a total of 24 students who would play checkers or chess.
- The teacher had a total of 26 students who would play checkers or backgammon.
Step 2: Use a Venn diagram to visualize the information
Create a Venn diagram with three circles representing backgammon, checkers, and chess. We'll label the overlapping regions based on the information given.
Start by labeling the intersection of all three circles with 5, representing the 5 students who would play all 3 games. Then, label the regions where only two games intersect based on the given information:
- 3 students would play checkers and backgammon, so label that intersection with 3.
- 2 students would play backgammon and chess, so label that intersection with 2.
- 1 student would play chess and checkers, so label that intersection with 1.
Step 3: Use the Venn diagram to find the number of students who would play only one game
- To find the number of students who would play only backgammon, look at the backgammon circle. Deduct the number of students in the intersection regions and the students who would play all 3 games. The remaining number represents the students who would play only backgammon.
- To find the number of students who would play only checkers and only chess, follow the same process.
Step 4: Calculate the number of students in the study hall
- To find the number of students in the study hall, subtract the students who wouldn't play any games from the total number of students in the class.
By following these steps, you should be able to find the answers to your questions.