# 2011 AMC 12A Problems/Problem 1

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## 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

~savannahsolver

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