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 <math>20</math> dollars.  
 
The base price of Michelle's cell phone plan is <math>20</math> dollars.  
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.  
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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 exceeded past 30 hours.
 
<math>30.5-30=.5</math> hours <math>=30</math> minutes.
 
<math>30.5-30=.5</math> hours <math>=30</math> minutes.
 
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.
 
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.

Revision as of 19:01, 19 August 2021

Problem

A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay?

$\textbf{(A)}\ 24.00 \qquad \textbf{(B)}\ 24.50 \qquad \textbf{(C)}\ 25.50 \qquad \textbf{(D)}\ 28.00 \qquad \textbf{(E)}\ 30.00$


Solution

The base price of Michelle's cell phone plan is $20$ dollars. If she sent $100$ text messages and it costs $5$ cents per text, then she must have spent $500$ cents for texting, or $5$ dollars. She talked for $30.5$ hours, but $30.5-30$ will give us the amount of time exceeded past 30 hours. $30.5-30=.5$ 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 $3$ dollars. Adding $20+5+3$ dollars $=28$ dollars $=\boxed{\textbf{D}}$.

Video Solution

https://youtu.be/tWz5T2Db9AY

~savannahsolver

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
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
2011 AMC 10A (ProblemsAnswer KeyResources)
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 10 Problems and Solutions

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