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.


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!

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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.
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