pamela leutwyler. there are 100 people at a party. everyone owns a house or a boat. everyone owns a...
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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
0
0
0
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 B
C
0
0
0
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 B
C
0
0
0
11
ab
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
0
0
0
11
ab
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
0
0
0
11
ab
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
0
0
0
11
ab
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
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
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
11
ab
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
0
0
0
11
ab
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
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
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
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
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
11
ab
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
0
0
0
11
ab
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
0
0
0
11
18b
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
0
0
0
11
18b
c
d
a + d = 40d = 22a + 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
0
0
0
11
18b
c
22
a + d = 40d = 22a + 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
0
0
0
11
18b=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
0
0
0
11
1832
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
0
0
0
11
1832
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
0
0
0
11
1832
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
0
0
0
11
1832
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
0
0
0
11
1832
17
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
0
0
0
11
1832
17
a + d = 40
a + b = 50
a + c = 35
a = 18
22
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
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
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
11
1832
17
a + d = 40
a + b = 50
a + c = 35
a = 18
J
913
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
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:
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' 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'B'
H'B'
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'B'
H'B'
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'B'
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'B'
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'B'
C'
11
If H J thenJ 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'B'
C'
11 J 13
13 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'B'
C'
11 J13
p
q r
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?_________
J13
r
s
H'B'
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'
C'
p
q
11
r + s = 27
J13s
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'
C'
p
q
11
r + s = 27
J13s
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'
C'
p
q
11
r + s = 27
J13s
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'
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
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'
C'
p
q
11
r + s = 27
J13s
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'
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
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'
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
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'
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
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'
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
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'
C'
32
17
11 J139
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? 27
18
B'
C'
32
17
11 J139
H'
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