Part i. We are told that the cost for 3 throws is 1 dollar. This means that if "x" is the number of throws then the total cost must be:
[tex]C(x)=\frac{1\text{ dollar}}{3\text{ throws}}x[/tex]
We can rewrite it in a simpler form as:
[tex]C(x)=\frac{1}{3}x[/tex]
If we purchased the armband then this cost is equivalent to (1/6) of a dollar per throw plus the cost of the armband, we get:
[tex]C_2(x)=\frac{1}{6}x+10[/tex]
Part ii. The graph of the two equations are two lines in the plane, like this:
In the graph, the red line represents the cost without the armband and the blue line represents the cost with the armband.
Part iii. We can see from the graph that if the number of throws is smaller than 60, then the cost is smaller without the armband, but if the cost is greater than 60 then the cost is smaller with the armband. Therefore, it makes sense to buy the armband if the number of throws is going to be greater than 60.
