Question

At Bike Shop X it costs ​$ 1.75 per hour plus a ​$ 3.00 deposit to rent a bike. At Bike Shop Z it costs ​$ 0.75 per hour plus a ​$10 deposit to rent a bike. The total​ 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 hours you have to rent the bike for the cost to be the same.

Answer 1

To find how many hours you have to rent the bike for the cost to be the same at Bike Shop X and Bike Shop Z, set the two equations representing their total costs equal to each other and solve for n. The number of hours required is approximately 9.33.

Step-by-step explanation:

The total cost, c, of renting a bike for n hours at Bike Shop X can be represented by the equation c = 1.75n + 3. The total cost, c, of renting a bike for n hours at Bike Shop Z can be represented by the equation c = 0.75n + 10. To find how many hours you have to rent the bike for the cost to be the same, you need to set the two equations equal to each other and solve for n.

1.75n + 3 = 0.75n + 10

Subtract 0.75n from both sides: 0.75n - 0.75n + 3 = 0.75n - 0.75n + 10

Combine like terms: 3 = 10 - 0.75n

Subtract 10 from both sides: 3 - 10 = 10 - 10 - 0.75n

Combine like terms: -7 = -0.75n

Divide both sides by -0.75: -7 / -0.75 = -0.75n / -0.75

Simplify: 9.333333333333334 = n

So, you would have to rent the bike for approximately 9.33 hours for the cost to be the same at both bike shops.