2007 AMC 12A Problems and Solution
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?
= the amount Pam spent = the amount Susan spent
Pam pays 10 more dollars than Susan
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?
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
The larger of two consecutive odd integers is three times the smaller. What is their sum?
Solution 1 Let be the smaller term. Then
; Thus, the answer is
; By trial and error, 1 and 3 work. 1+3=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?
Last year Mr. Jon Q. Public received an inheritance. He paid in federal taxes on