# Flute Rentals

## Statement of Situation

Jane is interested in renting a flute. She visits two flute shops and receives two offers. The first shop, "Heavenly Sounds" offered to her a fixed cost of \$200 and \$10 per month. The second shop, "Enchanted Notes" offered her a fixed cost of \$100 and \$15 per month.

## Identification of Variables

Independent Variable: Number of Months = n

Dependent Variable: Total Cost (\$) = C

## Equations

Heavenly Sounds: C = 10n + 200

Enchanted Sounds: C = 15n + 100

*C = Total Cost (\$)

*n = Number of Months

## Significance of the Point of Intersection

In this situation the Point of Intersection represents the break even point, so where both flute rental shops will have the same cost for the same number of months. Specifically, for this situation the point of intersection is at (20,400). This means at 20 months , both flute rental shops will have a total cost of \$400

## Summary Statement

To conclude, the break even point of both flute rental shops is at 20 months where the cost is \$400. I would suggest if Jane wants to rent a flute for 20 months or less she should rent from "Enchanted Notes", as the price will be cheaper. If Jane wants to rent the flute for 20 months or more should rent from "Heavenly Sounds", as the price will be cheaper.