let
x = the cost of the cabinet
y = the cost of a chair
z = the cost of a table
A cabinet, 4 chairs and 2 tables cost $825
x + 4y + 2z = 825
The cabinet costs 3 times as much as a chair
x = 3y
The table costs $120 more than a chair
z = 120 + y
by solving the system of equations
x + 4y + 2z = 825
x = 3y
z = 120 + y
we find
x = $195