Question

Carmen purchased a prepaid phone card for $25. Long distance calls cost 23 cents a minute using this card. Carmen used her card only once to make a long distance call. If the remaining credit on her card is $13.96, how many minutes did her call last?

Answer 1

So Carmen has initially $25 available on her prepaid phone card, but after making the long distance call, she only has $13.96 left. How much must she have spent on that call then?

Answer 2

When you know how much she has spent on the entire call, we can figure out how many minutes the call lasted. It is given that it costs 23 cents per minute. If you figured out the question I asked above, you know how much she spent on the call. That call lasted an unknown number of minutes, but in total it costed ... dollars. By dividing the total cost on the cost per minute, you get number of minutes.

Answer 3

You might wonder why you have to divide. Let me show you a trick you can use to see that dividing the total cost on the cost per minute gives minutes. If we write it in terms of units:
cost divided by cost per minute = cost/(cost/minute).
cost in the numerator cancels cost in the denumerator, so we are left with
cost/(cost/minute) = 1/(1/minute)
1/(1/minute) = minute (think for example 1/(1/2) = 1/(0.5) = 2)
Therefore, we get the number of minutes the call lasted by dividing the total cost of the call by the cost per minute.