You are choosing between two different cell phone plans. The first plan charges a rate of 21 cents per minute. The second plan charges a monthly fee of \( \$ 49.95 \) plus 9 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. \( C_{1}= \) If you talk for decimal place).

To define the costs of each cell phone plan, we can set up the equations as follows: The first plan charges \( 21 \) cents per minute, so the cost equation is: \[ C_{1} = 0.21t \] The second plan has a monthly fee of \( \$ 49.95 \) plus \( 9 \) cents per minute, leading to the cost equation: \[ C_{2} = 49.95 + 0.09t \] To find the number of talk minutes that produce the same cost for both plans, we can set these two equations equal to each other: \[ 0.21t = 49.95 + 0.09t \] Now, solve for \( t \): \[ 0.21t - 0.09t = 49.95 \] \[ 0.12t = 49.95 \] \[ t = \frac{49.95}{0.12} \] \[ t = 416.25 \] So, if you talk for approximately **416.25 minutes**, both plans will cost the same.