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MAA AMC
AMC 12/AHSME
1968 AMC 12/AHSME
14
14
Part of
1968 AMC 12/AHSME
Problems
(1)
What's y?
Source: 1968 AHSME Problem #14
9/7/2011
If
x
x
x
and
y
y
y
are non-zero numbers such that
x
=
1
+
1
y
x=1+\dfrac{1}{y}
x
=
1
+
y
1
and
y
=
1
+
1
x
y=1+\dfrac{1}{x}
y
=
1
+
x
1
, then
y
y
y
equals:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
x
−
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
1
−
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
1
+
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
−
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
x
<span class='latex-bold'>(A)</span>\ x-1 \qquad <span class='latex-bold'>(B)</span>\ 1-x \qquad <span class='latex-bold'>(C)</span>\ 1+x \qquad <span class='latex-bold'>(D)</span>\ -x \qquad <span class='latex-bold'>(E)</span>\ x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
x
−
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
1
−
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
1
+
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
−
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
x
ratio
AMC