Pamela Leutwyler. There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All.

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Presentation transcript:

Pamela Leutwyler

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C 0 0

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C 0 0 0

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 a + b = 50

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 a + b = 50 a + c = 35

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 a + b = 50 a + c = 35 a + b + c + d + 11 = 100 a + b + c + d = 89

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 a + b = 50 a + c = 35 a + b + c + d = 89

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 a + b = 50 a + c = 35 a + b + c + d = 89

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 d = 40 – a a + b = 50 b = 50 – a a + c = 35 c = 35 – a a + b + c + d = 89

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 d = 40 – a a + b = 50 b = 50 – a a + c = 35 c = 35 – a a + b + c + d = 89 a + 50 – a + 35 – a + 40 – a = 89 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a b c d a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C b c d a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C b c d a + d = 40 d = 22 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C b c 22 a + d = 40 d = 22 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C b=32 c 22 a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C c 22 a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C c=17 22 a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a + d = 40 a + b = 50 a + c = 35 a = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a + d = 40 a + b = 50 a + c = 35 a = 18 22

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a + d = 40 a + b = 50 a + c = 35 a = J

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a + d = 40 a + b = 50 a + c = 35 a = J =87

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a + d = 40 a + b = 50 a + c = 35 a = 18 J 9 13

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H B C a + d = 40 a + b = 50 a + c = 35 a = 18 J

Here is a different way to do The same problem:

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' if B  H = U then B'  H' = 

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' H'H' B'B' C'C' C'C' or ?

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' H'H' B'B' C'C' C'C' or 11

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' C'C' 11

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' C'C' 11

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' C'C' 11 If H  J then J  H J

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' C'C' 11 J do not have jobs.

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ H'H' B'B' C'C' 11 J 13 p qr s

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ J 13 r s H'H' B'B' C'C' p q 11 r+s+13=40 r + s = 27

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ r B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ r B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ r B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50 r + q = 35

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ r B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50 r + q = 35 p + q + r + s + 11 = 87 p + q + r + s = 76

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ r B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50 r + q = 35 p + q + r + s = 76

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ r B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50 r + q = 35 p + q + r + s = – r + 35 – r + r + 27 – r = – 2r = 76 r = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ 18 B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50 r + q = 35 p + q + r + s = – r + 35 – r + r + 27 – r = – 2r = 76 r = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ 18 B'B' C'C' p q 11 r + s = 27 J 13s H'H' r + p = 50 r + q = 35 p + q + r + s = – r + 35 – r + r + 27 – r = – 2r = 76 r = 18

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ 18 B'B' C'C' p=32 q=17 11 J 13s=9 H'H' p + q + r + s = – r + 35 – r + r + 27 – r = – 2r = 76 r = 18 r + s = 27 r + p = 50 r + q = 35

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car?_________ 18 B'B' C'C' J 139 H'H'

There are 100 people at a party. Everyone owns a house or a boat. Everyone owns a house or a car. 11 own neither a car nor a boat. All of the homeowners have jobs. 87 have jobs. 40 have a car and a boat. 50 have a house and a car. 35 have a house and a boat. How many have a job, a boat, and a car? B'B' C'C' J 139 H'H'