# Ticket prices at an Amusement park

A holiday themed amusement park recently opened for the winter season, and there are two ways for people to purchase their tickets. Option A is buying the tickets at the park gates for \$28.00 per ticket plus a base cost of \$10.00 for the donation drive to help a charity. Option B is ordering online for \$30.00 per ticket with a donation already included in the price. Which option is a better deal?..It depends on how many tickets are purchased

## Equations

Let c represent the cost (y value). Let t represent the number of tickets purchased (x value).

Option A: Ax+By+C=0 : 28t - C + 10=0

Option B: y=mx+b : C=30t

## Graphic Solution and the Point of Intersection

The point of intersection is at (5, 150). To test if these numbers are actually the graphical solution, subsistute t=5 and C=150 in to the equations of C=30t, and 28t - C + 10=0. This is because the POI gives us the solution, as the points lie on both of the lines.

Since the coordinates of the point of intersection, 5 and 150 satisfies both of the

equations, this means that t=5 and C=150 is the graphical solution.

## Significance of the Solution for this Linear system

This solution is significant because it will help people choose which option best suits their situation of how many tickets they are buying. If they are purchasing 4 or less tickets it is best to go with ordering tickets online (option B), because it will be a lower cost than purchasing them at the gates. If they are buying 5 tickets it will be the same cost, for both options, so it does not matter which option they choose to get their tickets. However, if they are buying 6 or more tickets the better choice is to purchase them at the park gates(option A), as the price would then be lower than buying it online.