You are choosing between two different cell phone plans. The first plan charges a rate of 25 cents per minute. The second plan charges a monthly fee of $44.95 plus 12 cents per minute.
Let  be the number of minutes you talk and  and  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.

Let $ t $ be the number of minutes you talk.

- **Plan 1**: Charges 25 cents per minute, so the cost is directly proportional to the number of minutes. The equation for Plan 1 is:

\[
C_1(t) = 0.25t
\]

- **Plan 2**: Charges a monthly fee of $44.95 plus 12 cents per minute. The equation for Plan 2 is:

\[
C_2(t) = 44.95 + 0.12t
\]

Now, to find the number of talk minutes that would produce the same cost for both plans, set the equations equal to each other:

\[
0.25t = 44.95 + 0.12t
\]

Solve for $ t $:

1. Subtract $ 0.12t $ from both sides:

\[
0.25t - 0.12t = 44.95
\]

\[
0.13t = 44.95
\]

2. Divide both sides by 0.13:

\[
t = \frac{44.95}{0.13} = 345
\]

So, the number of talk minutes that would produce the same cost for both plans is **345 minutes**.

### Do you want further details or have any questions about the solution?

Here are five related questions to expand your understanding:

1. How much would you pay with each plan if you talk for 200 minutes in a month?
2. What is the cost difference if you talk for 400 minutes under both plans?
3. How does the cost of Plan 1 compare to Plan 2 if you only talk for 100 minutes?
4. At what number of minutes does Plan 2 become more cost-effective than Plan 1?
5. How would the break-even point change if the monthly fee in Plan 2 increased to $50?

**Tip**: For these types of problems, setting the equations equal helps find the break-even point where both options cost the same!

You are choosing between two different cell phone plans. The first plan charges a rate of 25 cents per minute. The second plan charges a monthly fee of $44.95 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.

Learn how to compare two cell phone plans by solving linear equations. This problem involves creating equations for plan costs and finding the break-even point where both plans cost the same. Perfect for students in Grades 8-10 learning algebra and cost comparison.

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