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 adults (a) Number of children (c) Total people (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 adults (a) Number of children (c) Total people (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 adults (a) Number of children (c) Total people (t = a + c)
1 2 Multiples of Six
5 10
6 12
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
Number of adults (a)
Number of children (c)
Total people (t = a + c)
We can continue to fill in the table in order to determine whether or not a pattern exists for the total number of people at the show.
1 2
3
5 10
15
6 12
18
4
5
. . .
20
25
. . .
24
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
Number of adults (a)
Number of children (c)
Total people (t = a + c)
By examining the columns of the table, let a represent the number of adults at the show. Looking at the middle column, the number of children, c, can be represented as…
1 2
3
1x5 2x5 3x5
5 10
15
6 12
18
4
5
. . .
4x5
5x5
20
25
. . .
24
30
. . .
a x 5 … OR c = 5a
Multiples of Six
a
ax5
5a
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
Number of adults (a)
Number of children (c)
Total people (t = a + c)
By looking at the last column representing the total number of people at the show, we see each entry is a multiple of 6.
1 2
3
5 10
15
6 12
18
4
5
. . .
20
25
. . .
24
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 (D) 30
Number of adults (a)
Number of children (c)
Total people (t = a + c)
The total number of people at the show is also given by the number of adults plus the number of children.
Algebraically, this is given by t = a + 5a = 6a
1 2
3
5 10
15
6 12
18
4
5
. . .
20
25
. . .
24
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 (D) 30
Number of adults (a)
Number of children (c)
Total people (t = a + c)
t = 6a also reinforces that conclusion that the total number of people at the show must be a multiple of 6 or 6 divides the total people.
1 2
3
5 10
15
6 12
18
4
5
. . .
20
25
. . .
24
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 (D) 30
Number of adults (a)
Number of children (c)
Total people (t = a + c)
t = 6a also reinforces that conclusion that the total number of people at the show must be a multiple of 6 or 6 divides the total people.
1 2
3
5 10
15
6 12
18
4
5
. . .
20
25
. . .
24
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 Returning to original (B) 80 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. Multiples of Six 30 is a multiple of 6.
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 80 is not a multiple of 6, (B) 80 6 = 13 1/3 since 6 does not divide evenly into 80. (C) 36 (D) 30
Therefore, (B) is the answer.
Multiples of Six