Question

You ride an express bus from the center of town to your street. You have two payment options. Option A is to buy a monthly pass for $50 and pay $2 per ride.

Option B is to pay $4.50 per ride. After how many rides will the total costs of the two options be the same? Write a system of equations in order to solve this problem.
Answer the following questions in order making sure you number your answers:
1. What does × represent in the equation?
2.) What does y represent in the equation?
3.) What is the equation for Option A?
You will need to type the equation
4.) What is the equation for Option B?
You will need to type the equation
5.) What is the solution? Remember I need your solution (answer) in an ordered pair (x,y)

Answer 1

1. In the equation, "x" represents the number of rides taken.
2. In the equation, "y" represents the total cost of transportation.
3. The equation for Option A is: y = 2x + 50
4. The equation for Option B is: y = 4.5x
5. To find the number of rides for which the total cost of transportation is the same for both options, we need to set the two equations equal to each other:

2x + 50 = 4.5x

Subtracting 2x from both sides, we get:

50 = 2.5x

Dividing both sides by 2.5, we get:

x = 20

Therefore, the total costs of the two options will be the same after 20 rides. To find the total cost for this number of rides, we can plug x = 20 into either equation:

Option A: y = 2(20) + 50 = 90
Option B: y = 4.5(20) = 90

So the solution is (20, 90), which means after 20 rides, the total cost of both options will be $90.