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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1986 AMC 12/AHSME
20
20
Part of
1986 AMC 12/AHSME
Problems
(1)
Percentage algebra
Source: AHSME 1986 problem 20
10/1/2011
Suppose
x
x
x
and
y
y
y
are inversely proportional and positive. If
x
x
x
increases by
p
%
p\%
p
%
, then
y
y
y
decreases by
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
p
%
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
p
1
+
p
%
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
100
p
%
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
p
100
+
p
%
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
100
p
100
+
p
%
<span class='latex-bold'>(A)</span>\ p\%\qquad<span class='latex-bold'>(B)</span>\ \frac{p}{1+p}\%\qquad<span class='latex-bold'>(C)</span>\ \frac{100}{p}\%\qquad<span class='latex-bold'>(D)</span>\ \frac{p}{100+p}\%\qquad<span class='latex-bold'>(E)</span>\ \frac{100p}{100+p}\%
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
p
%
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
1
+
p
p
%
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
p
100
%
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
100
+
p
p
%
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
100
+
p
100
p
%
AMC