Question

Can someone help me?

Answer 1

$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