Tutorial
If there are exactly 5 times as many
children as adults at a show, which of
the following CANNOT be the number
of people at the show?
(A) 102
(B) 80
(C) 36
(D) 30
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36
(D) 30
The total number of people, t, at the show
depends on the number of adults, a, plus the
number of children, c.
Algebraically this can be represented by the
equation, t = a + c
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36
(D) 30
We can find some possible values for the
total number of people at the show by
making an organized table.
Number of Number of Total people
adults (a) children (c) (t = a + c)
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36
(D) 30
If there is only one adult at the show, then there must be five children.
This is true because there are exactly five times as many children as
adults AND 1 x 5 = 5 children.
This makes 6 total people at the show.
Number of Number of Total people
adults (a) children (c) (t = a + c)
1 5 6
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36
(D) 30
If there are two adults at the show, then there must be ten children.
OR 2 x 5 = 10 children.
This makes 12 total people at the show.
Number of Number of Total people
adults (a) children (c) (t = a + c)
1 5 6
2 10 12
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36 Number of Number of Total people
(D) 30
adults (a) children (c) (t = a + c)
1 5 6
We can continue to fill
2 10 12
in the table in order to
determine whether or 3 15 18
not a pattern exists for
the total number of 4 20 24
people at the show.
5 25 30
. . .
. . .
. . .
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36 Number of Number of Total people
(D) 30
adults (a) children (c) (t = a + c)
1 1x5 5 6
By examining the
columns of the table, 2 2x5 10 12
let a represent the
number of adults at the 3 3x5 15 18
show.
Looking at the middle 4 4x5 20 24
column, the number of
children, c, can be 5 5x5 25 30
represented as… .
.
.
.
.
.
. . .
a x 5 … OR a ax5 5a
c = 5a
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36 Number of Number of Total people
(D) 30
adults (a) children (c) (t = a + c)
1 5 6
By looking at the last 2 10 12
column representing the
total number of people 3 15 18
at the show, we see 4 20 24
each entry is a multiple
of 6. 5 25 30
. . .
. . .
. . .
a 5a
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36 Number of Number of Total people
(D) 30
adults (a) children (c) (t = a + c)
The total number of people 1 5 6
at the show is also given by
the number of adults plus 2 10 12
the number of children.
3 15 18
Algebraically, this is given
by t = a + 5a = 6a 4 20 24
5 25 30
. . .
. . .
. . .
a + 5a = 6a
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36 Number of Number of Total people
(D) 30
adults (a) children (c) (t = a + c)
1 5 6
t = 6a also reinforces
that conclusion that the 2 10 12
total number of people
at the show must be a 3 15 18
multiple of 6 or 6 divides 4 20 24
the total people.
5 25 30
. . .
. . .
. . .
a 5a 6a
Multiples of Six
Tutorial
If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the
number of people at the show?
(A) 102
(B) 80
(C) 36 Number of Number of Total people
(D) 30
adults (a) children (c) (t = a + c)
1 5 6
t = 6a also reinforces
that conclusion that the 2 10 12
total number of people
at the show must be a 3 15 18
multiple of 6 or 6 divides 4 20 24
the total people.
5 25 30
. . .
. . .
. . .
a 5a 6a
Multiples of Six
Tutorial
If there are exactly 5 times as many children
as adults at a show, which of the following
CANNOT be the number of people at the
show?
(A) 102 = 6 x 17
(B) 80 Returning to original
problem, we wish to find
(C) 36 = 6 x 6 which of the numbers to the
(D) 30 = 6 x 5 left are not multiples of 6.
36 is a multiple of 6.
102 is a multiple of 6. 30 is a multiple of 6.
Multiples of Six
Tutorial
If there are exactly 5 times as many children
as adults at a show, which of the following
CANNOT be the number of people at the
show?
(A) 102
(B) 80 6 = 13 1/3 since 6 does not divide
80 is not a multiple of 6,
(C) 36 evenly into 80.
(D) 30
Therefore, (B) is the answer.
Multiples of Six