Question

rentals at bike shop x it costs $2.75 per hour plus a $3.00 deposit to rent a bike. at bike shop z it costs $1.75 per hour plus a $7.00 deposit to rent cost, c, of renting a bike for n hours at either bike shop can be represented by an equation. write and solve a system of equations to find how many hou the bike for the cost to be less to rent a bike from bike shop x.
a.

b.

c.

d.

rentals at bike shop x it costs $2.75 per hour plus a $3.00 deposit to rent a bike. at bike shop z it costs $1.75 per hour plus a $7.00 deposit to rent

Explanation:

Step1: Define variables and equations

Let $n$ = number of hours, $C$ = total cost.
For Bike Shop X: $C = 2.75n + 3.00$
For Bike Shop Z: $C = 1.75n + 7.00$

Step2: Set equations equal (cost equality)

To find when costs are equal, set the two expressions for $C$ equal:
$2.75n + 3 = 1.75n + 7$

Step3: Solve for $n$

Subtract $1.75n$ from both sides:
$2.75n - 1.75n + 3 = 7$
$n + 3 = 7$

Subtract 3 from both sides:
$n = 7 - 3$
$n = 4$

Step4: Interpret the result

For $n > 4$ hours, the cost at Bike Shop Z is less than at Bike Shop X. The intersection point of the two lines (cost equality) is at $n=4$, $C=2.75(4)+3=14$, so $(4,14)$. This matches graph option C.

Answer:

C (the graph with lines intersecting at (4,14)), and you need to rent the bike for more than 4 hours for Shop Z to be cheaper. The number of hours where costs are equal is 4.