2011 AMC 12A Problem 1

Attempt Problem 1 of the 2011 AMC 12A 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 2011 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

A cell phone plan costs $20\$20 each month, plus 55¢ per text message sent, plus 1010¢ for each minute used over 3030 hours. In January Michelle sent 100100 text messages and talked for 30.530.5 hours. How much did she have to pay?
$24.00\$24.00
$24.50\$24.50
$25.50\$25.50
$28.00\$28.00
$30.00\$30.00
Answer: D
Concepts:moneyunit conversion
Small hint:
30.530.5 hours is 3030 minutes over the 3030-hour allowance
Big hint:
Add the base fee, 55¢ times the texts, and 1010¢ times the overage minutes
Solution:
The text charge is 100⋅5=500100 \cdot 5 = 500 cents =$5.= \$5. She talked 3030 minutes past the 3030-hour allowance, so the overage is 30⋅10=30030 \cdot 10 = 300 cents =$3.= \$3.
The total is $20+$5+$3=$28.\$20 + \$5 + \$3 = \$28.
Thus, the correct answer is D.
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