Which Hotel Should You Pick?
Pick the better deal!
Hotel Empire vs. Hotel Diamond
Hotel Empire has a booking cost of $150.00 and an additional cost of $25 per day.
Hotel Diamond has a booking cost of $250 and an extra cost of $15 per day. Which hotel deal is the best?
Let's Figure it Out!
Hotel Empire: C = 25d + 150
Hotel Diamond: C = 15d + 250
c is the total cost and is the dependent variable because it depends on the number of days you will be staying.
d is the number of days you'll be staying and it is the independent variable.
Since there is an initial booking cost this is a partial variation.
Realistically...
Hotel Empire: 3 Day Stay
C = 150 + 25(3)
Hotel Diamond: 3 Day Stay
C = 250 + 15(3)
Cost Difference
295 - 225 = 70
A $70 difference for a 3 day stay between Hotel Empire and Hotel Diamond.
Equations of Each Hotel's Cost Line In Y-Intercept Form
Hotel Empire: y = 25x + 150
Hotel Diamond: y = 15x + 250
25(10) + 150 y = 15(10) + 250
250 + 150 y = 150 + 250
400 = 400
A linear system!
Point of Intersection: (10, 400)
So What Does the POI Mean?
At 10 days the the cost of staying at Hotel Empire or Hotel Diamond is the same, $400 dollars.
How Does this Help You?
Now, you can see that if you want a hotel room for less than 10 days, Hotel Diamond is the better deal, however if you want a hotel room for more than 10 days, Hotel Empire is cheaper.