One ticket to a show costs20 at full price. Susanbuys 4 tickets using a coupon that gives her a 25%discount.Pam buys 5 tickets using a coupon thatgives her a 30% discount.How many more dollarsdoes Pam pay than Susan?2007 AMC 10 A, Problem #1—“Find the total cost for Susan and Pam”SolutionAnswer (C):Susan pays(4)(0.75)(20)=60dollars.Pam pays(5)(0.70)(20) = 70dollars, so she pays70-60 = 10more dollars thanSusan.Difficulty:EasyNCTM Standard:Problem Solving Standard: Apply and adapt a variety of appropriate strategiesto solve problems.Mathworld.com Classification:Number Theory>Arithmetic>Fractions>Percent
Definea@b=ab-b2anda#b=a+b-ab2. Whatis[email protected]6#2?2007 AMC 10 A, Problem #2—“Set up the two equation witha= 6, andb= 2”SolutionAnswer (A):The value of[email protected]is6·2-22= 12-4 = 8, and the valueof6#2is6 + 2-6·22= 8-24 =-16. Thus[email protected]6#2=8-16=-12.Difficulty:Medium-easyNCTM Standard:Algebra Standard: Understand patterns, relations, and functions.Mathworld.com Classification:Number Theory>Arithmetic
An aquarium has a rectangular base that measures100 cm by 40 cm and has a height of 50 cm.It isfilled with water to a height of 40 cm. A brick with arectangular base that measures 40 cm by 20 cm anda height of 10 cm is placed in the aquarium. By howmany centimeters does the water rise?2007 AMC 10 A, Problem #3—“The volume of water level rises is equal to the volumeof the brick.”SolutionAnswer (D):The brick has a volume of40·20·10 = 8000cubiccentimeters. Suppose that after the brick is placed in the tank, the waterlevel rises byhcentimeters. Then the additional volume occupied in theaquarium is100·40·h= 4000hcubic centimeters. Since this must be thesame as the volume of the brick, we have8000 = 4000handh= 2centimetersDifficulty:MediumNCTM Standard:Geometry Standard: analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.Mathworld.com Classification:Geometry>Solid Geometry>Volume
The larger of two consecutive odd integers is threetimes the smaller. What is their sum?2007 AMC 10 A, Problem #4—“Set up an equation to represent the relation of thetwo integers.”SolutionAnswer (A):Let the smaller of the integers bex. Then the larger isx+ 2. Sox+ 2 = 3x, from whichx= 1. Thus the two integers are 1 and3, and their sum is 4.Difficulty:EasyNCTMStandard:AlgebraStandard:representandanalyzemathematicalsituationsandstructures using algebraic symbols.Mathworld.com Classification:Number Theory>Integers>Odd number
A school store sells 7 pencils and 8 notebooks for4.15.It also sells 5 pencils and 3 notebooks for1.77.How much do 16 pencils and 10 notebookscost?
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