2004 AMC 8 Problem 12
Attempt Problem 12 of the 2004 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
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?
Small hint:
One hour of talking uses as much battery as several idle hours.
Big hint:
The phone was idle for hours and used for hour.
Solution:
When not in use, her cell phone uses up of its battery per hour. When it is in use, it uses up of its battery per hour.
Niki’s phone has been on for hours, with of those hours being idle and hour being used to talk on the phone.
This means that the phone has used up of its battery. In order to drain the remaining of the battery, the phone can last for more hours without being used.
Thus, B is the correct answer.
Problem 12 in other years
- 1985 AMC 8
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