Difference between revisions of "2011 AMC 12A Problems/Problem 1"
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== Solution == | == Solution == | ||
| − | The base price of Michelle's cell phone plan is < | + | The base price of Michelle's cell phone plan is <math>20</math> dollars. |
| − | If she sent 100 text messages and it costs 5 cents per text, then she must have spent 500 cents for texting, or < | + | If she sent <math>100</math> text messages and it costs <math>5</math> cents per text, then she must have spent <math>500</math> cents for texting, or <math>5</math> dollars. She talked for <math>30.5</math> hours, but <math>30.5-30</math> will give us the amount of time that she has to pay an additional amount for. |
| − | 30.5-30=.5 hours=30 minutes. | + | <math>30.5-30=.5</math> hours <math>=30</math> 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 < | + | Since the price for phone calls is <math>10</math> cents per minute, the additional amount Michelle has to pay for phone calls is <math>30*10=300</math> cents, or <math>3</math> dollars. |
| − | Adding < | + | Adding <math>20+5+3</math> dollars <math>=28</math> dollars <math>=\boxed{\textbf{D}}</math>. |
== See also == | == See also == | ||
{{AMC12 box|year=2011|before=First Problem|num-a=2|ab=A}} | {{AMC12 box|year=2011|before=First Problem|num-a=2|ab=A}} | ||
Revision as of 02:40, 10 February 2011
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 dollars.
If she sent text messages and it costs cents per text, then she must have spent 
cents for texting, or dollars. She talked for hours, but 
will give us the amount of time that she has to pay an additional amount for.
hours 
minutes.
Since the price for phone calls is cents per minute, the additional amount Michelle has to pay for phone calls is 
cents, or 
dollars.
Adding 
dollars 
dollars 
.
See also
| 2011 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by First Problem |
Followed by Problem 2 |
| 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 AMC 12 Problems and Solutions | |
