question in description

Question

Molly is supposed to call her friend every Thursday night. Sometimes they have a lot to talk about, other times not so much. There are two phone companies she can use: TCC charges $0.10 per minute (no matter how long the call). UFC charges $0.50 for the first minute plus $0.08 for every minute thereafter. How many minutes can Molly talk to be charged the same amount by either phone company?

Answer 1

let x = number of minutes of the phone call

 

cost for TCC = 0.10x

 

cost for UFC = 0.50 + 0.08(x - 1)

 

We are looking for the value of x so that

 0.10x = 0.50 + 0.08(x - 1)

0.10x = 0.50 + 0.08x - 0.08

0.02x = 0.42

       x = 21 minutes

 

The costs are the same for a 21 minute phone call.

 

 

Answer 2

Johnny,

 

Here's the CORRECT answer (as opposed to the incorrect one I gave you before).  Sorry for the confusion.

 

The trick with word problems is to take the information they give you and turn it into equations, and then solve. They want you to find the number of minutes for which the calls cost the same. So start by assigning a variable name to the number of minutes, m.

So the cost of a TCC call is .10 m.

And the cost of a UFC call is .50 + .08 (m - 1).

 

The (m - 1) is there because the first minute is already accounted for by the .50.  Only the additional minutes AFTER the first one get charged .08, so you have to subtract 1 from the number of minutes charged at .08.

So in order to find out how many minutes long a call would be that costs the same in both cases, you just want to set these two formulas equal to each other and see what m comes out to -- that is, solve for m

.10 m = .50 + .08 (m - 1)

 

Simplify:

.10 m = .50 + .08 m - .08

.10 m = .42 + .08 m

Subtract .08 m from each side:
.02 m = .42

Divide both sides by .02:
m = 21

So the answer is 21 minutes.