Question

the cost of renting a canoe to use on river y costs $23. the cost of renting a canoe to use on river z costs $2 per hour plus a $13 deposit. the total cost, c, of renting a canoe on either river for n hours can be represented by an equation. write and graph a system to find how many hours you have to rent a canoe for the cost to be the same on both rivers.
graph the system of equations. choose the correct answer below.

Explanation:

Step1: Define cost equations

River Y: $c=23$; River Z: $c=2n+13$

Step2: Find intersection (equal cost)

Set $23=2n+13$
Subtract 13: $23-13=2n$ → $10=2n$
Solve for $n$: $n=\frac{10}{2}=5$

Step3: Verify graph properties

• $c=23$ is a horizontal line at $c=23$.
• $c=2n+13$ has y-intercept $(0,13)$ and passes through $(5,23)$. This matches graph B.

Answer:

1. System of equations:

River Y: $c=23$
River Z: $c=2n+13$

1. Correct graph: Option B
2. Hours for equal cost: 5