Question

If A,B,C are positive integers such that A+B+C+AB+BC+AC+ABC=100
then A+B+C????​

Answer 1

abc+ab+bc+ca+a+b+c=1000

then what is the value of a+b+c

The solution to this problem begins by adding 1 to both sides of the equation.

So,

abc+ab+bc+ca+a+b+c+1=1000+1

This can be reduced to,

ab.(c+1)+b.(c+1)+a.(c+1)+(c+1)=1001

This can be further reduced to,

(c+1).(ab+b+a+1)=1001

Which reduces to,

(a+1).(b+1).(c+1)=7×11×13

Since exact values of a,b,c

are not required, so order of factors is not important, so in any order,

a=7−1=6

b=11−1=10

a=13−1=12

∴a+b+c=6+10+12=28