Let's break down the problem step by step to solve it.

We are given two phone plans:

• Plan 1: No monthly fee but charges $0.17 per minute.
• Plan 2: Has a $20 monthly fee and charges $0.12 per minute.

We need to find the number of minutes (let's call it $x$) at which both plans will cost the same.

Cost of Plan 1:

The total cost for Plan 1 is simply the cost per minute multiplied by the number of minutes: $\text{Cost of Plan 1} = 0.17x$

Cost of Plan 2:

The total cost for Plan 2 includes a fixed monthly fee of $20 and $0.12 per minute: $\text{Cost of Plan 2} = 20 + 0.12x$

Set the two costs equal:

To find when the costs are equal, we set the equations equal to each other: $0.17x = 20 + 0.12x$

Solve for $x$:

1. Subtract $0.12x$ from both sides: $0.17x - 0.12x = 20$ $0.05x = 20$

2. Divide both sides by 0.05: $x = \frac{20}{0.05} = 400$

So, the two plans will cost the same when the customer uses 400 minutes of calls.

Would you like more details or have any questions?

Here are five related questions you could explore:

1. What would the cost of each plan be for 500 minutes of calls?
2. If the monthly fee for Plan 2 increases to $25, how would that change the number of minutes at which the plans are equal?
3. How would the answer change if Plan 1 charged $0.20 per minute instead of $0.17?
4. What is the total cost for Plan 2 if no minutes are used?
5. How would the total cost for each plan change if only 300 minutes were used?

Tip: When comparing two different plans with a fixed cost and a variable cost, it's often helpful to set up an equation and solve for the point where the costs are equal to make an informed decision!