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!