Question

Customers of a phone company can choose between two service plans for long distance calls. The first plan has an $18 monthly fee and charges an additional $0.15 for each minute of calls. The second plan has a $12 monthly fee and charges an additional $0.20 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 1

120 minutes

Explanation:

Let x be the number of minutes of calls made in a month.

For the first plan, the monthly cost is $18 + $0.15x.

For the second plan, the monthly cost is $12 + $0.20x.

To find the point where the costs are equal, we need to solve the equation:

18 + 0.15x = 12 + 0.20x

Subtracting 0.15x from both sides gives:

18 = 12 + 0.05x

Subtracting 12 from both sides gives:

6 = 0.05xDividing both sides by 0.05 gives:

x = 120

Therefore, the costs of the two plans will be equal for 120 minutes of calls.

Answer 2

Let's call the number of minutes of calls "x".

For the first plan, the cost will be:

Cost = $18 + $0.15x

For the second plan, the cost will be:

Cost = $12 + $0.20x

To find the point at which the costs of the two plans are equal, we can set the two equations equal to each other and solve for x:

$18 + $0.15x = $12 + $0.20x

Subtracting $12 from both sides, we get:

$6 + $0.15x = $0.20x

Subtracting $0.15x from both sides, we get:

$6 = $0.05x

Dividing both sides by $0.05, we get:

x = 120

Therefore, if a customer makes more than 120 minutes of calls per month, the first plan with the $18 monthly fee and $0.15 per minute charge will be more cost-effective. If a customer makes less than 120 minutes of calls per month, the second plan with the $12 monthly fee and $0.20 per minute charge will be more cost-effective.