Let's define the number of minutes of calls as $x$.

Plan A:

• Fixed cost: $22
• Variable cost: $0.11 per minute

The total cost for Plan A can be expressed as: $\text{Cost of Plan A} = 22 + 0.11x$

Plan B:

• Fixed cost: $14
• Variable cost: $0.15 per minute

The total cost for Plan B can be expressed as: $\text{Cost of Plan B} = 14 + 0.15x$

Finding the amount of calling where the two plans cost the same:

To find the number of minutes where both plans cost the same, we set the two cost expressions equal to each other and solve for $x$:

$22 + 0.11x = 14 + 0.15x$

Subtract 14 from both sides: $8 + 0.11x = 0.15x$

Subtract $0.11x$ from both sides: $8 = 0.04x$

Solve for $x$ by dividing both sides by 0.04: $x = \frac{8}{0.04} = 200$

So, the two plans cost the same when you make 200 minutes of calls.

Cost when the two plans cost the same:

To find the cost, substitute $x = 200$ into either cost equation (both should give the same result):

Using Plan A's cost equation: $\text{Cost of Plan A} = 22 + 0.11(200) = 22 + 22 = 44$

So, when the two plans cost the same, the cost is $44.

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Would you like more details on this solution or have any other questions? Here are some related questions to explore:

1. How would the costs change if Plan B had a lower per-minute rate?
2. What if Plan A had a lower fixed cost?
3. How many minutes should one talk to make Plan A cheaper than Plan B?
4. How do the costs differ if the number of minutes is 100?
5. How would you graph the cost of both plans?
6. What if a third plan was introduced with a different cost structure?
7. How does a change in fixed cost affect the break-even point?
8. How would rounding of costs to the nearest cent affect the results?

Tip: When comparing costs in similar scenarios, it's often useful to express both cost structures algebraically and find the intersection point for a clear comparison.