Answer
(a) $C(x)=0.50x-10$
(b) Talking for 105 minutes would cost 42.5 dollars, and talking for 120 minutes would cost 50 dollars.
Work Step by Step
If we look at the linear formula y=mx+b, we can see that b can represent the fixed price while m represents the rate per minute. We also must take into account the 80 minutes that are included, so we can model the exercise in the following equation:
$C(x)=0.50(x-80)+30$
Simplifying would give:
$C(x)=0.50x-40+30$
$C(x)=0.50x-10$
To find the costs of talking for 105 and 120 minutes, we calculate C(105) and C(120) respectively:
$C(105)=0.50(105)-10$
$C(105)=52.5-10$
$C(105)=42.5$ dollars
$C(120)=0.50(120)-10$
$C(120)=60-10$
$C(120)=50$ dollars
