Question

The CEO of the new LopeLand amusement park wants to make sure the park's ticket prices are comparable to another park across town, Jackrabbit Farm. Jackrabbit Farm offers three different ticket packages. Two tickets and two all-day ride passes cost $56. Three tickets and two all-day ride passes cost $68. Four tickets and three all-day ride passes cost $92. Set up an equation for each package that relates the price of a ticket y to the price of an all-day ride pass x. Write all three equations as y in terms of x.

1) Graph the three equations in one graph.

2) Is there a solution to the system of equations? Explain any assumptions you made in setting up the system that were not true.

3) Find the points of intersection and list them as ordered (x,y) pairs. You can use Goal Seek or solve by hand. What do the intersection points on the graph mean in the context of the ticket and pass prices?

4) Considering the intersection points, is there one that you think would be the best to set the prices at Lopeland? Explain your choice.

Answer 1

Let price of a ticket be y and all day ride pass be x

case1 : 2x +2y = 56 ; x+y = 28

case 2: 3y + 2x = 68

case 3 : 4y + 3x = 92

The point of intersection give :

case 2 and case 2 are (4, 20) means price of package 2 and 3 are same when price of day pass = $4 and a ticket is $20

Package 1 and package 2 are same when price of day pass = $ 16 and ticket price is $ 12

Package 1 and package 3 are same when price of day pass = $ 20 and ticket price is $ 8