1. Pamela Leutwyler

2. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________

3. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ D L E 12

4. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ D L E 12 P

5. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ D L E 12 P 0 0

6. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ D L E 12 0 0 P

7. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ D L E 12 0 0 P 15

8. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ D L E 12 0 0 P 15 a b c d e

9. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ D L E 12 0 0 P 15 a b c d e a+b = 14

10. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P d e a+b = 14 D L 12 15 a b c a+b+c = 27

11. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P d e a+b = 14 D L 12 15 a b c a+b+c = 27 c = 13

12. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P d e D L 12 15 a b 13

13. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P d e D L 12 15 a b 13 b = 9

14. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P d e D L 12 15 a 9 13 a = 5

15. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P d e D L 12 15 5 9 13

16. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P d = 12 e D L 12 15 5 9 13

17. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P 12 e=13 D L 12 15 5 9 13

18. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___________ E 0 0 P 12 13 D L 12 15 5 9 13

19. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___30_______ E 0 0 P 12 13 D L 12 15 5 9 13

20. At a college reunion: Everyone who is a doctor or a lawyer drives a Porsche. All those who are neither doctors nor lawyers are engineers. 12 are doctors and lawyers and engineers. 17 are doctors and engineers. 13 are engineers and lawyers. 45 are doctors or lawyers. 57 drive Porsches. 31 are doctors. 35 are lawyers. 43 are engineers. How many engineers drive Porsches?___30_______ E 0 0 P 12 13 D L 12 15 5 9 13