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The problem involves two cell phone plans, and you're asked to determine at what point the second plan becomes less expensive. Let's define the costs of both plans as a function of the number of minutes used.

### Plan 1:
- The first plan charges 24 cents per minute.
- Cost equation for Plan 1: 
  \[
  C_1 = 0.24 \times m
  \]
  where $m$ is the number of minutes used.

### Plan 2:
- The second plan has a monthly fee of $29.95 plus 12 cents per minute.
- Cost equation for Plan 2: 
  \[
  C_2 = 29.95 + 0.12 \times m
  \]

### Solution:
To find out when Plan 2 becomes cheaper, we need to solve for $m$ when the cost of Plan 2 equals the cost of Plan 1:
\[
0.24m = 29.95 + 0.12m
\]
First, subtract $0.12m$ from both sides:
\[
0.12m = 29.95
\]
Now, solve for $m$:
\[
m = \frac{29.95}{0.12} \approx 249.58
\]

### Answer:
You would need to use approximately **250 minutes or more** for the second plan to be less expensive than the first.

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:
1. What if Plan 2 had a lower monthly fee but a higher per-minute charge?
2. How would the result change if Plan 1 charged a different rate per minute?
3. How does the solution change if both plans had monthly fees?
4. What happens if you estimate more or fewer minutes of usage in a month?
5. Can this problem be solved using a graphing method for linear equations?

**Tip:** Always set up a system of equations to compare two linear pricing models.

You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents per minute. The second plan charges a monthly fee of $29.95 plus 12 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? Round your answer to the nearest minute.

Learn how to compare two cell phone plans using linear equations. This problem involves determining the number of minutes needed for a monthly plan to be less expensive. Suitable for students in Grades 9-10.

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