### Student Page3.5.3Systems of Equations in Context: Renting Bicycles A4US

Four different bike rental companies are competing for your business on Mackinac Island. Which one gives the best deal for the number of hours you plan to rent a bike?

This activity helps you determine the best deal. It also helps you make sense of the importance of domain and range both in context and without a context.

When you finish the Systems of Equations in Context: Renting Bicycles activity, answer the following questions for Section 3.5:

• How can you solve a system of two linear equations in two unknowns graphically?

• How can you also solve a system algebraically?

You and your friends plan to rent bikes while visiting Mackinac Island.

• Island Rentals charges a base fee of $16 plus$6 per hour per bike.

##### (a)

How are the charges from these bike rental companies similar to the charges for Island Rentals and Bikes Unlimited?

##### (b)

Find equations for each company. Record slopes, intercepts, and equations in the table.

##### (d)

Compare the graphs of these two companies with those above. What do you notice?

#### 5.

##### (b)

In the context of bike rentals, what aspects of the bike rental make the lines modeling the rental charges parallel?

#### 6.

Write and answer two questions related to bike rentals and the fees the four companies above charge.