Question

You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents per minute. The second plan charges a monthly fee of $34.95 plus 12 cents per minute.
Let
t
be the number of minutes you talk and
C
1
and
C
2
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

Answer:

$C_{1}(t) = 0.24*t$

$C_{2}(t) = 34.95 + 0.12*t$

291.25 talk minutes would produce the same cost for both plans.

Step-by-step explanation:

Both plans can be modeled by a first order equation in the following format:

$C(t) = C_{0} + f*t$

In which $C_{0}$ is the initial cost, f is the fee that is paid for each minute, and t is the number of minutes.

Cost of the first plan:

The problem states that the first plan charges a rate of 24 cents per minute, which means that $f = 0.24$.There is no initial cost, so $C_{0} = 0$.

The equation for this plan is:

$C_{1}(t) = 0.24*t$

Cost of the second plan:

The problem states that the second plan charges a monthly fee of $34.95 plus 12 cents per minute. So $C_{0} = 34.95$ and $f = 0.12$

The equation for this plan is:

$C_{2}(t) = 34.95 + 0.12*t$

Find the number of talk minutes that would produce the same cost for both plan:

This is the instant t in which:

$C_{1}(t) = C_{2}(t)$

$0.24t = 34.95 + 0.12t$

$0.12t = 34.95$

$t = \frac{34.95}{0.12}$

$t = 291.25$

291.25 talk minutes would produce the same cost for both plans.