Question

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $23 monthly fee and charges an additional $0.12 for each minute of calls. The second plan has no monthly fee but charges $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 1

Okay.

The only way to answer this question is to know the monthly fee and the charge per minute for each plan. Let's do an example to see how this would work.
Suppose the first plan has no monthly fee but charges 10 cents per minute, and the second plan charges a $10 monthly fee plus 2 cents per minute. Let x represent the number of minutes for which the two plans cost the same. The cost for x minutes under the first plan would be 10x cents. The cost for x minutes under the second plan would be 1000 + 2x cents (notice that we rewrote the $10 monthly fee as 1000 cents, since all of the other costs have been written in terms of cents). Since x is the number of minutes for which these two plans cost the same, we can set these two costs equal to each other using an algebraic equation:
\[10x = 1000 + 5x\]


Now we solve for x:
\[5x = 1000\]
(subtract 5x from both sides)
\[x = 200\]
(divide both sides by 200)
So our answer is 200 minutes. Let's check if this is right. Under the first plan, 200 minutes would cost (200)(10) = 2000 cents, or $20. Under the second plan, we would have to pay an initial $10, then (200)(5) = 1000 cents, or $10, for 5 cents per minutes. Altogether, the second plan would also cost $20, so our answer is correct.
Your question can be solved in the same way.

Answer 2

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