Problem:
Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for hours. If she is using it constantly, the battery will last for only hours. Since the last recharge, her phone has been on hours, and during that time she has used it for minutes. If she doesn't talk any more but leaves the phone on, how many more hours will the battery last?
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Solution:
The phone has been used for minutes, or hour, to talk, during which time it has used of the battery. In addition, the phone has been on for hours without talking, which used an additional or of the battery. Consequently, of the battery has been used, meaning that of the battery, or hours remain if Niki does not talk on her phone.
Niki's battery has hours of potential battery life. By talking for one hour, she uses hours of battery life. In addition, the phone is left on and unused for hours, using an additional hours. This leaves hours of battery life if the phone is on and unused.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions