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:
Mediumeasy
NCTM Standard:
Problem Solving Standard: apply and adapt a variety of appropriate strategies
to 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:
Medium
NCTM Standard:
Problem Solving Standard: apply and adapt a variety of appropriate strategies
to 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)40,000
2007 AMC 10 A, Problem #7—“Find out the percentage10,500 in the inheritance.”
Difficulty:
Medium
NCTM
Standard:
Algebra
Standard:
represent
and
analyze
mathematical
situations
and
structures using algebraic symbols.
Mathworld.com Classification:
Number Theory
>
Arithmetic
>
Fractions
>
Percent
Triangles
ABC
and
ADC
are isosceles with
AB
=
BC
and
AD
=
DC
.
Point
D
is inside
4
ABC
,
∠
ABC
= 40
◦
, and
∠
ADC
= 140
◦
.
What is the
degree measure of
∠
BAD
?
(A)
20
(B)
30
(C)
40
(D)
50
(E)
60
2007 AMC 10 A, Problem #8
—
“
∠
BAD
=
∠
BAC

∠
DAC
.”
Solution
Answer
(D):
Because
4
ABC
is
isosceles,
∠
BAC
=
1
2
(180
◦

∠
ABC
) = 70
◦
.
A
B
C
D
40
140
Similarly,
∠
DAC
=
1
2
(180
◦

∠
ADC
) = 20
◦
.
Thus
∠
BAD
=
∠
BAC

∠
DAC
= 50
◦
.
OR
Because
4
ABC
and
4
ADC
are isosceles triangles and
BD
bisects
∠
ABC
and
∠
ADC
, applying the Exterior Angle Theorem to
4
ABD
gives
∠
BAD
= 70
◦

20
◦
= 50
◦
.
Difficulty:
Medium
NCTM Standard:
Geometry Standard: analyze characteristics and properties of two and three
dimensional geometric shapes and develop mathematical arguments about geometric relationships.