2011 AMC 12A Problems/Problem 1

Problem

A cell phone plan costs dollars each month, plus cents per text message sent, plus cents for each minute used over hours. In January Michelle sent text messages and talked for hours. How much did she have to pay?

Solution

The base price of Michelle's cell phone plan is <dollar/>20. If she sent 100 text messages and it costs 5 cents per text, then she must have spent 500 cents for texting, or <dollar/>5. She talked for 30.5 hours, but 30.5-30 will give us the amount of time that she has to pay an additional amount for. 30.5-30=.5 hours=30 minutes. Since the price for phone calls is 10 cents per minute, the additional amount Michelle has to pay for phone calls is 30*10=300 cents, or <dollar/>3. Adding <dollar/>20+<dollar/>5+<dollar/>3=<dollar/>28=.