+0  
 
0
103
3
avatar

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?

 Jul 18, 2021
 #1
avatar+27 
+1

\(ab + c = bc + a\\ ab - bc = a-c \\ b(a-c) = a-c \\ b(a-c) - (a-c) = 0\\ (a-c)(b-1)=0\\ a=c\\ b=1 \)

Therefore, a and c must equal to 6.5, though the question states that all of these numbers are integers.

 Jul 18, 2021
 #2
avatar+1573 
+2

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?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

b = 1

ac + 1 = 41

ac = 40

a + c = 13

(40/c) + c = 13

c = 8,   c = 5

a + b + c = 14

 Jul 19, 2021
 #3
avatar+1548 
+3

1 * (5 + 8) = 13

 

1 + (5 * 8) = 41

 Jul 19, 2021

12 Online Users

avatar