Customers of a phone company can choose between two service plans for long distance calls. The first plan has no monthly fee but charges $0.16 or each minute of calls. The second plan has a $29 monthly fee and charges an additional $0.12 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

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 $0.16 or each minute of calls. The second plan has a $29 monthly fee and charges an additional $0.12 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 1

Let x be the number of minutes of calls.

For the first plan, the cost is 0.16x.
For the second plan, the cost is 29 + 0.12x.
Setting the costs equal to each other, we get 0.16x = 29 + 0.12x.
Subtracting 0.12x from both sides, we get 0.04x = 29.
Dividing both sides by 0.04, we get x = 725.
Thus, the costs of the two plans will be equal for 725 minutes of calls. Answer: \boxed{725}.

Answer 2

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $65,770, and the variable costs will be $9.50 per book. With the other method, the one-time fixed costs will total $17,700 and the variable costs will be $21 per book. For how many books produced will the costs from the two methods be the same?

Answer 3

Let x be the number of books produced.

For the first method, the cost is $65,770 + $9.50x.
For the second method, the cost is $17,700 + $21x.
Setting the costs equal to each other, we get $65,770 + $9.50x = $17,700 + $21x.
Subtracting $9.50x from both sides, we get $65,770 = $17,700 + $11.50x.
Subtracting $17,700 from both sides, we get $48,070 = $11.50x.
Dividing both sides by $11.50, we get x = $48,070 / $11.50.
Therefore, the costs from the two methods will be the same when approximately 4177 books are produced. Answer: \boxed{4177}.

Answer 4

Let's assume the number of minutes of calls as 'x'.

For the first plan, the cost can be calculated as:
Cost of plan 1 = $0.16 * x

For the second plan, the cost can be calculated as:
Cost of plan 2 = $29 + $0.12 * x

To find the number of minutes when the costs of the two plans are equal, we can set up the equation:

$0.16 * x = $29 + $0.12 * x

Simplifying the equation:

$0.16 * x - $0.12 * x = $29

$0.04 * x = $29

Now, we can solve for 'x':

x = $29 / $0.04

x = 725

Therefore, the costs of the two plans will be equal for 725 minutes of calls.