You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $49.95 plus 10 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).\begin{align*}
C_{1}&=\
C_{2}&=\
\end{align*}If you talk for minutes the two plans will have the same cost.
Q. You are choosing between two different cell phone plans. The first plan charges a rate of 22 cents per minute. The second plan charges a monthly fee of $49.95 plus 10 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).\begin{align*}
C_{1}&=\
C_{2}&=\
\end{align*}If you talk for minutes the two plans will have the same cost.
Write Equations: Let's first write down the equations for the cost of each plan in terms of the number of minutes talked, t. For the first plan, which charges 22 cents per minute, the cost C1 in dollars is given by: C1=0.22t
Cost Calculation: For the second plan, which charges a monthly fee of $49.95 plus 10 cents per minute, the cost C2 in dollars is given by:C2=49.95+0.10t
Set Equations Equal: To find the number of minutes that would produce the same cost for both plans, we need to set the two cost equations equal to each other and solve for t:0.22t=49.95+0.10t
Subtract and Combine: Subtract 0.10t from both sides of the equation to get all the terms involving t on one side:0.22t−0.10t=49.95
Divide and Solve: Combine like terms on the left side of the equation: 0.12t=49.95
Perform Division: Divide both sides of the equation by 0.12 to solve for t: t=0.1249.95
Round to One Decimal: Perform the division to find the value of t:t≈416.25
Round to One Decimal: Perform the division to find the value of t:t≈416.25Since we are asked to round the answer to one decimal place, we round t to:t≈416.3 minutes
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