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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?

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5 Answers

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.

Formula

SP - Cost = Profit

Cost can be Fixed Cost or Variable Cost

Selling Price = Cost per unit x number of units

Lets take the question and see what we have

Profit = $1125

Cost = Advertisement = $75 (in this case it can be considered Fixed Cost)

Number of tickets sold = $120

We do not know the price that is the unknown and we call it x

Now the Total selling Price is 120 times x = 120x

We can put all the numbers together to fit into the formulat

Selling Price - Cost = Profit

120x           - 75    = 1125         i.e. 120x-75=1125

Solve for x

we will move the numbers together by taking the -75 over the bridge

when we cross over the bridge the sign changes

So

120x  = 1125+75

120x  = 1200

What then is X

x is 1200 divided by 120

x = 1200/120 =10---->  $10 per ticket


Lets verify

$10 per ticket and 120 tickets = $1200 take in

Pay out advertising $75

What's left in your pocket 

$1200 - $75 = $1125

That's the profit $1125

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

Add 75 to each side

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,

x = $10 <==Answer