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Purple Comet Problems
2003 Purple Comet Problems
5
Problem 5, Fall 2003 , MS and HS
Problem 5, Fall 2003 , MS and HS
Source:
June 23, 2011
Problem Statement
Let
a
a
a
,
b
b
b
, and
c
c
c
be nonzero real numbers such that
a
+
1
b
=
5
a + \frac{1}{b} = 5
a
+
b
1
=
5
,
b
+
1
c
=
12
b + \frac{1}{c} = 12
b
+
c
1
=
12
, and
c
+
1
a
=
13
c + \frac{1}{a} = 13
c
+
a
1
=
13
. Find
a
b
c
+
1
a
b
c
abc + \frac{1}{abc}
ab
c
+
ab
c
1
.
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