You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $34.95 plus 10 cents per minute.

Question

You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $34.95 plus 10 cents per minute.Let  be the number of minutes you talk and  and  be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans (Round your answer to one decimal place).

Answer 1

C1(t) = 0.22 t

C2(t) = 34.95 + 0.1t

0.22t = 34.95 + 0.1t

22t = 3495 + 10t

12t = 3495

t = 291.25

C1(291.25) = 64.075

C2(291.25) = 34.95 + 291.25*.1 = 34.95 + 29.125 = 64.075

The will cost the same after 291.25 minutes, or 4 hours 51 minutes and 15 seconds

Anytime after that, the second plan is cheaper