pamela leutwyler. there are 100 people at a party. everyone owns a house or a boat. everyone owns a...

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?_________



H B

C



H B

C

0

0



H B

C

0

0

0



H B

C

0

0

0

11



H B

C

0

0

0

11

ab

c

d



H B

C

0

0

0

11

ab

c

d

a + d = 40



H B

C

0

0

0

11

ab

c

d

a + d = 40

a + b = 50



H B

C

0

0

0

11

ab

c

d

a + d = 40

a + b = 50

a + c = 35



H B

C

0

0

0

11

ab

c

d

a + d = 40

a + b = 50

a + c = 35

a + b + c + d + 11 = 100

a + b + c + d = 89



H B

C

0

0

0

11

ab

c

d

a + d = 40

a + b = 50

a + c = 35

a + b + c + d = 89



H B

C

0

0

0

11

ab

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



H B

C

0

0

0

11

ab

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



H B

C

0

0

0

11

ab

c

d

a + d = 40

a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

18b

c

d

a + d = 40

a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

18b

c

d

a + d = 40d = 22a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

18b

c

22

a + d = 40d = 22a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

18b=32

c

22

a + d = 40

a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

1832

c

22

a + d = 40

a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

1832

c=17

22

a + d = 40

a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

1832

17

22

a + d = 40

a + b = 50

a + c = 35

a = 18



H B

C

0

0

0

11

1832

17

a + d = 40

a + b = 50

a + c = 35

a = 18

22



H B

C

0

0

0

11

1832

17

a + d = 40

a + b = 50

a + c = 35

a = 18

22

J



H B

C

0

0

0

11

1832

17

a + d = 40

a + b = 50

a + c = 35

a = 18

22

J

913

11+17+32+18+9=87



H B

C

0

0

0

11

1832

17

a + d = 40

a + b = 50

a + c = 35

a = 18

J

913



H B

C

0

0

0

11

1832

17

a + d = 40

a + b = 50

a + c = 35

a = 18

J

913

27

Here is a different way to do The same problem:



H'B' if B H = U

then B' H' =



H'B'

H'B'

C'

C'

or

?



H'B'

H'B'

C'

C'

or

11



H'B'

C'

11



H'B'

C'

11

If H J thenJ H

J



H'B'

C'

11 J 13

13 do not have jobs.



H'B'

C'

11 J13

p

q r

s



J13

r

s

H'B'

C'

p

q

11

r+s+13=40 r + s = 27



r

B'

C'

p

q

11

r + s = 27

J13s

H'r + p = 50



r

B'

C'

p

q

11

r + s = 27

J13s

H'r + p = 50

r + q = 35



r

B'

C'

p

q

11

r + s = 27

J13s

H'r + p = 50

r + q = 35

p + q + r + s + 11 = 87

p + q + r + s = 76



r

B'

C'

p

q

11

r + s = 27

J13s

H'r + p = 50

r + q = 35

p + q + r + s = 76



r

B'

C'

p

q

11

r + s = 27

J13s

H'r + p = 50

r + q = 35

p + q + r + s = 76 50 – r + 35 – r + r + 27 – r = 76 112 – 2r = 76 r = 18



18

B'

C'

p

q

11

r + s = 27

J13s

H'r + p = 50

r + q = 35

p + q + r + s = 76 50 – r + 35 – r + r + 27 – r = 76 112 – 2r = 76 r = 18



18

B'

C'

p=32

q=17

11 J13s=9

H'

p + q + r + s = 76 50 – r + 35 – r + r + 27 – r = 76 112 – 2r = 76 r = 18

r + s = 27

r + p = 50 r + q = 35



18

B'

C'

32

17

11 J139

H'


How many have a job, a boat, and a car? 27

18

B'

C'

32

17

11 J139

H'

pamela leutwyler. there are 100 people at a party. everyone owns a house or a boat. everyone owns a...

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