Answer:
The average cost is less than 100 when the number of items x is greater than 2
Step-by-step explanation:
The cost equation is [tex]C(x) = 10x + 180[/tex]
The average cost [tex]Cp = \frac{C(x)}{x}[/tex]
We want to know when the cost Cp is less than 100.
So
[tex]Cp <100[/tex]
[tex]Cp = \frac{C(x)}{x} <100[/tex]
[tex]10 + \frac{180}{x} <100\\\\\frac{180}{x} <90[/tex]
For [tex]x> 0[/tex]
[tex]\frac{180}{90} <x[/tex]
[tex]x> 2[/tex]
The average cost is less than 100 when [tex]x>2[/tex]
