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# A theater made a profit of \$1,125 from showing a movie. The theater sold 120 tickets and spent \$75 on advertising. How much did each ticket cost?

You are given the following:     Profit (P) = \$1,125

Cost (C) on advertising = \$75

# of tickets sold = 120 tickets

Price per ticket = \$? ==>

Note:   the price per ticket multiplied by the # of tickets sold yields the total revenue.

Profit, cost, and revenue are related by the following formula:

Profit = Revenue - Cost

Let x represent the price per ticket, then....

....   Revenue = (# of tickets sold) * (price per ticket) = (120) * (x) = 120x

So,

Profit = Revenue - Cost

1,125 = 120x - 75

Now solve for x:

1,125 + 75 = 120x - 75 + 75

1,200 = 120x

(1,200) / 120 = (120x) / 120

10 = x

Thus, each ticket cost \$10.

Profit = Revenue - Cost

We have the following information

Profit : 1125, Cost = 75, We need to find Revenue ?

Revenue = Total number of tickets sold X Price per ticket (P).

Revenue = 120 X P = 120P

Now lets plug all the information we have in our original equation

Profit = Revenue - Cost

1125 = 120P - 75

Change the sides changes the sign

1125+75 = 120P

1200 = 120 P

Divide each side by 120

10 = P

Therefore the price  (P) of each ticket is \$10.

This story problem requires a simple equation for profit.  The equation can be written:

Profit = Cost per ticket X Number of tickets - Fixed cost

For this problem, the variables (Profit, Cost per ticket, Number of tickets, and Fixed cost) are defined as follows:

Profit = \$1,125

Cost per ticket = x (variable being sought)

Number of tickets = 120

Fixed cost = \$75

Substituting in the variables produces the equation (without dollar signs)

1,125 = 120x - 75

1200 = 120x

Divide both sides by 120

x = 10

Each ticket cost \$10.

Profit = revenue - cost

1,125 = 120x - 75, where x is the cost of each ticket.

Solve for x,

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