Question:
Make a list of the different arrangements that Mrs. Buchanan could use.
Answer:
[tex](x,y) = \{(1,36),(2,18),(3,12),(4,9),(6,6)\}[/tex]
Step-by-step explanation:
Given
[tex]Members = 36[/tex]
[tex]Rows\ Limit = 6[/tex]
Represent the rows with x and the column, y.
This means that:
[tex]x * y = 36[/tex]
Make y the subject:
[tex]y = \frac{36}{x}[/tex]
The list is then generated as follows:
When x = 6.
[tex]y = \frac{36}{6} = 6[/tex]
[tex](x,y) = (6,6)[/tex]
When x = 5
[tex]y = \frac{36}{5} = 7.2[/tex]
This result can not be use because the result of the number of columns must be an integer
When x = 4
[tex]y = \frac{36}{4} = 9[/tex]
[tex](x,y) = (4,9)[/tex]
When x = 3
[tex]y = \frac{36}{3} = 12[/tex]
[tex](x,y) = (3,12)[/tex]
When x = 2
[tex]y = \frac{36}{2} = 18[/tex]
[tex](x,y) = (2,18)[/tex]
When x = 1
[tex]y = \frac{36}{1} = 36[/tex]
[tex](x,y) =(1,36)[/tex]
So, the possible list is:
[tex](x,y) = \{(1,36),(2,18),(3,12),(4,9),(6,6)\}[/tex]
