14. Mrs. Buchanan is planning marching routines for the school band. The band has 36 members. Band members can march in any number of rows as long as each row has the same number of members. The marching path, however, limits members to 6 per row.

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]

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QUICKK
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