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AMC 10
2000 AMC 10
20
Amc
Amc
Source:
February 22, 2006
Problem Statement
Let
A
A
A
,
M
M
M
, and
C
C
C
be nonnegative integers such that
A
+
M
+
C
=
10
A+M+C=10
A
+
M
+
C
=
10
. What is the maximum value of
A
⋅
M
⋅
C
+
A
⋅
M
+
M
⋅
C
+
C
⋅
A
A\cdot M\cdot C+A\cdot M+M\cdot C+C\cdot A
A
⋅
M
⋅
C
+
A
⋅
M
+
M
⋅
C
+
C
⋅
A
?
(A)
49
(B)
59
(C)
69
(D)
79
(E)
89
\text{(A)}\ 49 \qquad\text{(B)}\ 59 \qquad\text{(C)}\ 69 \qquad\text{(D)}\ 79\qquad\text{(E)}\ 89
(A)
49
(B)
59
(C)
69
(D)
79
(E)
89
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