Question

You are choosing between two different cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $39.95 plus 12 cents per minute. Let t 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

Answer:

285.28571429 minutes

Step-by-step explanation:

Let us represent

The number of minutes you talk = t

C1 = Cost in dollars of the first plan

C2 = Cost in dollars of the second plan

First plan

The first plan charges a rate of 26 cents per minute

Converting cents to dollars

100 cents = 1 dollars

26 cents =

26/100 cents

=$ 0.26

C1 = $0.26 × t

C1 = 0.26t .......... Equation 1

Second Plan

The second plan charges a monthly fee of $39.95 plus 12 cents per minute

Converting 12 cents to dollars

100 cents = 1 dollars

12 cents =

12/100

= $0.12

C2 = $39.95 + 0.12t........Equation 2

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

We would Equate C1 to C2

C1 = C2

0.26t = $39.95 + 0.12t

Collect like terms

0.26t - 0.12t = $39.95

= 0.14t = $39.95

Divide both sides by 0.14

= t = $34.95/0.14

t = 285.28571429 minutes

Therefore, the number of talk minutes that would produce the same cost for both plans is 285.28571429 minutes.