mock\

a+b=10
b+c=10
c+a=10
Then 2(a+b+c)=10+10+10
a+b+c=30/2
a+b+c=15

a+b=10, b+c=10 so a=c c+a=10 so 2a=10 so a=5, c=5 10-a=b 10-5=5

a=b=c 3a=15

Add all equations to get:- $2(a + b + c) = 30\\ a + b + c = \color{#69047E}{\boxed{15}}$

a+b=10 b+c=10 and c+a=10 you add them together and you get a+a+b+b+c+c=30 but since you only want one of each letter and there is 2 of each you divide it by 2. 30/2=15

$a+b=10$

$b+c=10$

$a+c=10$

$a+b+b+c+a+c=10+10+10=30$

$2a+2b+2c=30=2(a+b+c+$

$a+b+c=\frac {30}{2}$