Difference between revisions of "2004 AMC 8 Problems/Problem 12"
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she is using it constantly, the battery will last for only <math>3</math> hours. | she is using it constantly, the battery will last for only <math>3</math> hours. | ||
Since the last recharge, her phone has been on <math>9</math> hours, and during | Since the last recharge, her phone has been on <math>9</math> hours, and during | ||
| − | that time she has used it for <math>60</math> minutes. If she doesn’t | + | that time she has used it for <math>60</math> minutes. If she doesn’t use it any |
more but leaves the phone on, how many more hours will the battery last? | more but leaves the phone on, how many more hours will the battery last? | ||
| Line 11: | Line 11: | ||
==Solution== | ==Solution== | ||
| − | When not being used, the cell phone uses up <math>1 | + | When not being used, the cell phone uses up <math>\frac{1}{24}</math> of its battery per hour. When being used, the cell phone uses up <math>\frac{1}{3}</math> of its battery per hour. Since Niki's phone has been on for <math>9</math> hours, of those <math>8</math> simply on and <math>1</math> being used to talk, <math>8(\frac{1}{24}) + 1(\frac{1}{3}) = \frac{2}{3}</math> of its battery has been used up. To drain the remaining <math>\frac{1}{3}</math> the phone can last for <math>\frac{\frac{1}{3}}{\frac{1}{24}}=\boxed{\textbf{(B)}\ 8}</math> more hours without being used. |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2004|num-b=11|num-a=13}} | {{AMC8 box|year=2004|num-b=11|num-a=13}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 12:28, 29 January 2023
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 use it any
more but leaves the phone on, how many more hours will the battery last?
Solution
When not being used, the cell phone uses up 
of its battery per hour. When being used, the cell phone uses up 
of its battery per hour. Since Niki's phone has been on for hours, of those 
simply on and 
being used to talk, 
of its battery has been used up. To drain the remaining the phone can last for 
more hours without being used.
See Also
| 2004 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
