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2007AMC12AProblemsandSolution

By Derrick Williams,2014-06-03 23:37
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2007AMC12AProblemsandSolution

2007 AMC 12A Problems and Solution

    Problem 1

    One ticket to a show costs at full price. Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickets using a coupon that gives her a 30% discount. How many more dollars does Pam pay than Susan?

Solution

    = the amount Pam spent = the amount Susan spent

    ;

    ;

    Pam pays 10 more dollars than Susan

    Problem 2

    An aquarium has a rectangular base that measures 100 cm by 40 cm and has a

    height of 50 cm. It is filled with water to a height of 40 cm. A brick with a rectangular base that measures 40 cm by 20 cm and a height of 10 cm is placed in the aquarium. By how many centimeters does the water rise?

Solution

    The brick has volume . The base of the aquarium has area . For

    every inch the water rises, the volume increases by ; therefore, when the

    volume increases by , the water level rises

    Problem 3

    The larger of two consecutive odd integers is three times the smaller. What is their sum?

    Solution

    Solution 1 Let be the smaller term. Then

    ; Thus, the answer is

    Solution 2

    ; By trial and error, 1 and 3 work. 1+3=4.

    Problem 4

    Kate rode her bicycle for 30 minutes at a speed of 16 mph, then walked for 90

    minutes at a speed of 4 mph. What was her overall average speed in miles per hour?

    Solution

    ;

    ;

    Problem 5

    Last year Mr. Jon Q. Public received an inheritance. He paid in federal taxes on