Question

Black Diamond Ski Resort charges $50 for ski rental and $15 an hour to ski. Bunny Hill Ski Resort charges $75 for ski rental and $10 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.

Answer 1

Answer:

5 Hours

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

To Solve this problem we need to first create an equation for both resorts. Both Resorts have a fixed price which is added to a changing price that depends on the amount of hours the ski's were rented. We can use the variable x to represent the amount of hours rented, and the variable y to represent total charge.

Black Diamond Ski Resort: y = 50+15x

Bunny Hill Ski Resort: y = 75 + 10x

We now have an equation for both resorts to find the total price after a certain amount of hours. Now we want to know what what hour the prices of BOTH resorts will be the same. We can calculate this by equally both equations and solving for x, like so.

$50+15x = 75+10x$ ..... subtract 10x and 50x from both sides

$5x = 25$ ... divide both sides by 5

$x = 5$

Now we can see that if you rent the Ski's for 5 hours BOTH resorts will charge you the same amount.