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?(A)$4.76(B)$5.84(C)$6.00(D)$6.16(E)$6.322007 AMC 10 A, Problem #5—“Set up two equations to solve the cost of a pencil anda notebook.”Difficulty:Medium-easyNCTM Standard:Problem Solving Standard: apply and adapt a variety of appropriate strategiesto solve problems.Mathworld.com Classification:Algebra>Algebraic Equations>Linear Equation
At Euclid High School, the number of students takingthe AMC10 was 60 in 2002, 66 in 2003, 70 in 2004,76 in 2005, and 78 in 2006, and is 85 in 2007.Between what two consecutive years was there thelargest percentage increase?2007 AMC 10 A, Problem #6—“Find out the percentage increase for each year.”Difficulty:MediumNCTM Standard:Problem Solving Standard: apply and adapt a variety of appropriate strategiesto solve problems.Mathworld.com Classification:Number Theory>Arithmetic>Fractions>Percent
Last year Mr. John Q. Public received an inheritance.He paid 20% in federal taxes on the inheritance, andpaid 10% of what he had left in state taxes. He paida total of10,500 for both taxes. How many dollarswas the inheritance?(A)30,000(B)32,500(C)35,000(D)37,500(E)40,0002007 AMC 10 A, Problem #7—“Find out the percentage10,500 in the inheritance.”Difficulty:MediumNCTMStandard:AlgebraStandard:representandanalyzemathematicalsituationsandstructures using algebraic symbols.Mathworld.com Classification:Number Theory>Arithmetic>Fractions>Percent
TrianglesABCandADCare isosceles withAB=BCandAD=DC.PointDis inside4ABC,∠ABC= 40◦, and∠ADC= 140◦.What is thedegree measure of∠BAD?(A)20(B)30(C)40(D)50(E)602007 AMC 10 A, Problem #8—“∠BAD=∠BAC-∠DAC.”SolutionAnswer(D):Because4ABCisisosceles,∠BAC=12(180◦-∠ABC) = 70◦.ABCD40140Similarly,∠DAC=12(180◦-∠ADC) = 20◦.Thus∠BAD=∠BAC-∠DAC= 50◦.ORBecause4ABCand4ADCare isosceles triangles andBDbisects∠ABCand∠ADC, applying the Exterior Angle Theorem to4ABDgives∠BAD= 70◦-20◦= 50◦.Difficulty:MediumNCTM Standard:Geometry Standard: analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.