Question

You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per
minute. The second plan charges a monthly fee of $34.95 plus 10 cents per minute.
Lett be the number of minutes you talk and C₁ and C₂ 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).
C₁
C₂ =
If you talk for
minutes the two plans will have the same cost.

Answer 1

The equation for the cost of the first plan (C₁) in terms of t is:
C₁ = 0.23t

The equation for the cost of the second plan (C₂) in terms of t is:
C₂ = 34.95 + 0.10t

To find the number of talk minutes that would produce the same cost for both plans, we need to set the two equations equal to each other and solve for t:

0.23t = 34.95 + 0.10t

0.13t = 34.95

t = 34.95/0.13

t ≈ 268.85

Therefore, approximately 268.9 minutes of talk time would produce the same cost for both plans.