## The Situation

John wants to go to Wonderland next summer. He will be going by himself. He was on Canada's Wonderland's website and was thinking about some of the options he had. These were his 3 options:

1. Buy a season's pass without a parking pass
2. Buy a season's pass with a parking pass
3. Don't buy a season's pass or a parking pass

He will probably go to Wonderland once a week during his summer vacation. This means that he will be visiting Canada's Wonderland 8 times over the summer. Which option should he go with, 1, 2 or 3?

## What we Know

Wonderland Prices:

Parking Pass \$40

Season's Pass \$70

One-time Parking Fee \$20/visit

## Forming Equations

In the following equations let C represent cost & let x represent the number of visits

Situation 1 ► Season's Pass without a Parking Pass

C = Season's Pass + Parking Fee / visit

y = 20x + 70

Situation 2 ► Season's Pass with a Parking Pass

C = Season's Pass + Parking Pass

y = 70 + 40

y = 110

Situation 3 ► No Season's Pass or Parking Pass

C = Admission Fee / visit + Parking Fee / visit

C = \$40 / visit + \$20 / visit

C = (\$40 + \$20) / visit

C = \$60 / visit

y = 60x

## The Graph

The y-axis represents ► Money Spent (\$)

The x-axis represents ► Number of Visits

When I made the graph i divided all the equations by 10 to be able to represent the situation in an enhanced manner (visually). This way it is easier to pinpoint the locations at which these lines intercept.

Situation 1 is represented by the RED line

Situation 2 is represented by the BLUE line

Situation 3 is represented by the GREEN line

## Intersection

Where do these lines intersect and what does that mean?

Lines 1 and 2 intersect at (2,110).

Lines 1 and 3 intersect at (1.75,105)

Lines 2 and 3 intersect at (1.8,110)

The coordinates at which these lines meet mark the point at which it would cost John the same amount of money (x) as long as he took the specific number of visits (y) whether he took any of those 2 situations.

## What's the best Situation for John?

Since John is going to go to Wonderland 8 times over the summer, we can substitute x (number of visits) in every equation with 8 to figure out the cost.

Prices for every situation if John visits Wonderland 8 times:

Situation 1 ►

y = 20(8) + 70

y = 160 + 70

y = 230

Situation 2 ►

y = 110

Situation 3 ►

y = 60(8)

y = 480

We can clearly see that Situation 2 is the cheapest option for John.

John should buy both, a Season's Pass and a Parking Pass