# Snow Valley Ski Club

### By Hansneer Bhurji

Josh wants to join the Ski Club at Snow Valley Ski resort this winter season. He is considering two payment options:

Plan A - Standard Rate

\$50 per visit and No registration fee.

Plan B - Frequent Extremist

\$25 per visit plus \$100 registration fee.

Which payment option should Josh chose?

## Equation

Plan A -

slope = Δy/ Δx = 100-50/2-1 = 50/1= 50

y=50x

Where y= the total cost (dependent variable) and x= is the number of visits (Independent variable). Since there is no registration fee the line will start at (0,0).

Plan B-

slope = Δy/ Δx = 150-125/2-1 = 25/1= 25

y=25x+b

Where y= the total cost (dependent variable) and x= is the number of visits (Independent variable) and b= y-intercept (registration fee).

Therefore the equation is y=25x+100

## Intersection Point

The Intersection point in the graph is (4,200).

To find intersection point:

y=50x and y=25x +100

- find x

50x=25x+100

50x-25x=100

25x/25 = 100/25

x=4

- substitute x in equation

y=50x

y=50 (4)

y= 200

This point is significant because if Josh visits Snow Valley for 4 times he can chose any of the payment options since they will both cost him \$200 but if he goes less than 4 times Josh should chose Plan A because he would have to pay less. On the other hand if Josh goes more than 4 times he should chose Plan B.

## In conclusion.....

Both Plan A and Plan B will cost the same on the 4th visit.