You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per minute. The second plan charges a monthly fee of $44.95 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?

To determine how many minutes you would need to use in a month for the second plan to be preferable, we can set up an inequality. 

Let $ x $ represent the number of minutes used in a month.

### Cost of the first plan:
The first plan charges $ 23 $ cents per minute. Therefore, the cost for $ x $ minutes is:
\[
C_1 = 0.23x
\]

### Cost of the second plan:
The second plan charges a monthly fee of $ 44.95 $ dollars plus $ 12 $ cents per minute. Therefore, the cost for $ x $ minutes is:
\[
C_2 = 44.95 + 0.12x
\]

### Find when the second plan is preferable:
The second plan becomes preferable when its cost is less than the first plan's cost:
\[
44.95 + 0.12x < 0.23x
\]

### Solving the inequality:
1. Subtract $ 0.12x $ from both sides:
   \[
   44.95 < 0.11x
   \]
2. Divide both sides by $ 0.11 $ to solve for $ x $:
   \[
   x > \frac{44.95}{0.11}
   \]
   \[
   x > 408.64
   \]

### Conclusion:
You would need to use **more than 408.64 minutes** in a month for the second plan to be preferable. Since you can't use a fraction of a minute in this context, you would need to use at least **409 minutes** to make the second plan more cost-effective.

Would you like more details or have any questions?

Here are five related questions:
1. How would the solution change if the first plan charged 20 cents per minute?
2. What if the monthly fee in the second plan was $50.95 instead of $44.95?
3. How do changes in the per-minute rate of the second plan affect the breakeven point?
4. If you only used 300 minutes a month, which plan would be cheaper?
5. Can you create a function to represent the difference in costs between the two plans based on the number of minutes?

**Tip:** When comparing costs of different plans, always consider the fixed costs and the variable costs per unit to determine which plan is more economical based on your usage level.

Find out how many minutes you need to use in a month for the second cell phone plan to be cheaper than the first. Detailed cost analysis and inequality setup provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation