A theater sells tickets for a concert. Tickets for lower-level seats sell for $55 each, and tickets for upper-level seats sell for $30 each. The theater sells 241 tickets for $9,355.

How many tickets of each type were sold?

lower-level tickets

upper-level tickets

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

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step-by-step explanation:

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