You are choosing between two different cell phone plans. The first plan charges a rate of 18 cents per minute. The second plan charges a monthly fee of \( \$ 49.95 \) plus 8 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). \( C_{1}= \)

To find the cost of the first plan, we can use the formula: \[ C_{1} = 0.18t \] where \( t \) is the number of minutes talked. To find the cost of the second plan, we can use the formula: \[ C_{2} = 49.95 + 0.08t \] where \( t \) is the number of minutes talked. 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 \( t \): \[ 0.18t = 49.95 + 0.08t \] Now, let's solve for \( t \). Solve the equation by following steps: - step0: Solve for \(t\): \(0.18t=49.95+0.08t\) - step1: Move the variable to the left side: \(0.18t-0.08t=49.95\) - step2: Subtract the terms: \(0.1t=49.95\) - step3: Divide both sides: \(\frac{0.1t}{0.1}=\frac{49.95}{0.1}\) - step4: Divide the numbers: \(t=\frac{999}{2}\) The number of talk minutes that would produce the same cost for both plans is \( t = 499.5 \) minutes. Therefore, if you talk for 499.5 minutes, both plans would cost the same amount.