Friday, April 22, 2011

AMC12A 2011 Problem #1

I'm going to do math problems from various tests such as the AMC or the SAT on this blog, and hopefully it can help people out with tests. If there are any requests to do specific problems just leave them in the comments.
I'm starting off with problems from AMC12A that we had earlier this year. 

A cell phone plans costs $20 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?


Because the cell phone plan costs $20 each month, we can start out the cost at $20. Michelle sent 100 text messages in that month, and the cost of text messaging is 5 cents per text message. Thus, the extra cost from text messaging is $0.05*100 which is equal to $5.00. Now the total cost is $25. The problem states that there is an additional cost of 10 cents for each minute used over 30 hours. Michelle talked on the phone for 30.5 hours which means she spent an additional .5 hours or 30 minutes on the phone. Because the cost of an extra minute on the phone is 10 cents, we multiply $0.10*30 which equals $3.00. Now we add that to the total cost and we get $28.00.

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