2011 AMC 12A Problem 1

Below is the professionally curated solution for Problem 1 of the 2011 AMC 12A, 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.

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Concepts:moneyunit conversion

Difficulty rating: 840

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

Solution:

The text charge is 1005=500100 \cdot 5 = 500 cents =$5.= \$5. She talked 3030 minutes past the 3030-hour allowance, so the overage is 3010=30030 \cdot 10 = 300 cents =$3.= \$3.

The total is $20+$5+$3=$28.\$20 + \$5 + \$3 = \$28.

Thus, the correct answer is D.

Problem 1 in Other Years