Answer: Lower level tickets = 85
Upper level tickets = 156
Step-by-step explanation: The first thing we shall do is assign letters to the unknown variables. We'll start by calling the lower level tickets L, and the upper level tickets P.
Next is we use the clues we've been given. Since the theater sold 241 tickets, we can write the expression
L + P = 241 ---------------- (1)
Next thing we're told is that lower level tickets were sold for $55 while upper level tickets were sold for $30. If total ticket sales was $9355, then we can write another expression
55L + 30P = 9355 -------(2)
We now have a pair of simultaneous equations
L + P = 241 ---------------------(1)
55L + 30P = 9355 ---------(2)
From equation (1), we shall make L the subject of the equation
L = 241 - P
Substitute for the value of L in equation (2), we now have
55(241 - P) + 30P = 9355
13255 - 55P + 30P = 9355
Collecting like terms we now have
13255 - 9355 = 55P - 30P
(Note that when a positive value crosses from one side of the equation to the other side, it becomes negative, and vice versa.
3900 = 25P
Divide both sides of the equation by 25
156 = P.
This means upper level tickets sold were 156 in number.
Substitute for the value of P in equation (1)
L + P = 241
L + 156 = 241
Subtract 156 from both sides of the equation
L + 156 - 156 = 241 - 156
L = 85
Therefore, lower level tickets sold were 85 and
Upper level tickets sold were 156
