If a, b, and c are positive integers satisfying ab + c = bc + a = 13 and ac + b = 41, what is the value of a + b + c?
+48 \(ab + c = bc + a\\ ab - bc = a-c \\ b(a-c) = a-c \\ b(a-c) - (a-c) = 0\\ (a-c)(b-1)=0\\ a=c\\ b=1 \)
Therefore, a and c must equal to 6.5, though the question states that all of these numbers are integers.
+1694 If a, b, and c are positive integers satisfying ab + c = bc + a = 13 and ac + b = 41, what is the value of a + b + c?
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b = 1
ac + 1 = 41
ac = 40
a + c = 13
(40/c) + c = 13
c = 8, c = 5
a + b + c = 14
