$10 a month fixed plus $0.10 for each message.
Variable:
m - number of text messages per month
Function:
c(m) - cost per month in dollars of Text-Pay Plan for m messages
Answer: c(m) = 0.10 m + 10
The Frequent text plan costs $20 for 0 messages (that's the fixed cost) and has a slope of (30 - 20)/200 = 1/20 = 0.05 dollars per message.
f(m) = 0.05 m + 20
How many text messages per month make these equal?
c(m) = f(m)
0.10 m + 10 = 0.05 m + 20
0.10 m - 0.05 m = 20 - 10
0.05 m = 10
m = 10/0.05 = 200
Check:
c(200) = .1(200)+10 = 20+10 = 30
f(200) = .05(200) + 20 = 10 + 20 = 30, good
Answer: 200 messages