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2011 AMC 10A Problem 1

Problem 1 of 25EasierAlgebra

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?

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Solution

Michelle has to pay $20\$20 for the monthly fee. Her text messages cost 100⋅5=500100\cdot 5=500 cents, or $5.\$5. Finally she talked for 0.50.5 hours, 3030 minutes, over 3030 hours. This means her extra charge is 30⋅10=30030\cdot10=300 cents, or $3.\$3. Her total cost is $20+$5+$3=$28. \$20 + \$5 + \$3 = \$28. Thus, D is the correct answer.

More practice

Concepts: money · unit conversion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.