To help pay for the next school event, Terry and Tony want to make a
profit from ticket sales for this dance. They determine that they
would like to bring in a total of $475 from ticket sales.
a. If x represents the price per ticket, write an equation to represent
this situation.
b. Some student council dance committee members believe they should
charge $4.00 per ticket, while others think they should charge $4.50
per ticket. Terry and Tony believe the price per ticket should be
$5.00. Use substitution to find the solution to your equation from
part a and to determine how much each ticket should cost.

Then we also call [tex]N[/tex] the number of tickets sold: therefore, this total profit made by Terry and Tony from the ticket sale is the product between the tickets sold, N, and the price per ticket, x:

[tex]Nx[/tex]

And since they want to do a profit of P = $475, we can therefore write

[tex]Nx=475[/tex]

b)

The equation of part a) can be re-arranged as

[tex]N=\frac{475}{x}[/tex]

where N is the number of tickets sold and x the price per ticket.

The 1st group of student want to charge $4.00 per ticket, so

x = 4.00

And so the number of tickets that they should sell in this case is

[tex]N=\frac{475}{4.00}=118.8 \sim 119[/tex]

The 2nd group of student want to charge $4.50 per ticket, so

x = 4.50

And so the number of tickets that they should sell in this case is

[tex]N=\frac{475}{4.50}=105.6 \sim 106[/tex]

Terry and Tony want to charge $5.00 per ticket, so

x = 5.00

And so the number of tickets that they should sell in this case is

[tex]N=\frac{475}{5.00}=95[/tex]

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