Question: Customers of a phone company can choose between two service plans for long distance calls. The first plan has no monthly fee but charges $0.14 for each minute of calls. The second plan has a $21 monthly fee and charges an additional $0.10 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
1. **State the problem:** We want to find the number of minutes $m$ for which the cost of the two plans is the same.
2. **Define variables and costs:**
- Let $m$ be the number of minutes of calls.
- Cost of Plan 1: $0.14m$
- Cost of Plan 2: $21 + 0.10m$
3. **Set up the equation for equality:**
$$0.14m = 21 + 0.10m$$
4. **Solve for $m$:**
Subtract $0.10m$ from both sides:
$$0.14m - 0.10m = 21 + 0.10m - 0.10m$$
$$0.04m = 21$$
5. **Isolate $m$ by dividing both sides by $0.04$:**
$$m = \frac{21}{0.04}$$
Show cancellation:
$$m = \frac{21}{\cancel{0.04}} \times \frac{\cancel{1}}{1}$$
6. **Calculate the value:**
$$m = 525$$
7. **Interpretation:**
The costs of the two plans are equal when the customer makes 525 minutes of calls.