Question 6
Find the sum of all (not necessarily distinct) values of $a$ over all triples $(a,b,c)$ of real numbers that satisfy the equations:
$$(a+b)(c+1)=22\quad(1),$$
$$(a+c)(b+1)=22\quad(2),$$
$$(b+c)(a+1)=22\quad(3).$$
Numerical answer only; a non-negative integer less than 1000.
$$(a+b)(c+1)=22\quad(1),$$
$$(a+c)(b+1)=22\quad(2),$$
$$(b+c)(a+1)=22\quad(3).$$
Numerical answer only; a non-negative integer less than 1000.