Question

You take an express bus from the town center to your street. You have two fare options:

Option A: Purchase a monthly pass for $30 and pay $1 per ride.
Option B: Pay $2.50 for each ride.

A) Write an equation for the monthly cost (C) of Option A based on the number of rides (R).
B) Write an equation for the monthly cost (C) of Option B based on the number of rides (R).
C) After how many rides will the total costs of both options be the same?
D) After how many rides will Option B be more cost-effective than Option A?

Answer 1

The monthly cost (C) of Option A can be represented by the equation C = 30 + R * 1, where R is the number of rides. The monthly cost (C) of Option B can be represented by the equation C = R * 2.50.

The total costs of both options will be the same after 20 rides, and Option B will be more cost-effective than Option A when the number of rides is less than 20.

Step-by-step explanation:

A) Monthly cost (C) of Option A based on the number of rides (R):

The monthly cost of Option A consists of the $30 monthly pass plus an additional $1 for each ride, regardless of the number of rides taken. Therefore, the equation for the monthly cost (C) of Option A based on the number of rides (R) is:

C = 30 + R * 1

B) Monthly cost (C) of Option B based on the number of rides (R):

The monthly cost of Option B is simply $2.50 for each ride that is taken. Therefore, the equation for the monthly cost (C) of Option B based on the number of rides (R) is:

C = R * 2.50

C) Number of rides at which the total costs of both options are the same:

To find the number of rides at which the total costs of both options are the same, we set the equations for Option A and Option B equal to each other:

30 + R * 1 = R * 2.50

Simplifying this equation, we get:

30 = R * 2.50 - R

30 = R * (2.50 - 1)

30 = R * 1.50

To solve for R, we divide both sides of the equation by 1.50:

R = 30 / 1.50

R = 20

Therefore, the total costs of both options will be the same after 20 rides.

D) Number of rides at which Option B is more cost-effective than Option A:

To find the number of rides at which Option B is more cost-effective than Option A, we need to compare the total costs of both options. We can calculate the total cost of Option A by substituting the number of rides (R) into the equation for Option A:

Total cost of Option A = 30 + 1 * R

We can calculate the total cost of Option B by substituting the number of rides (R) into the equation for Option B:

Total cost of Option B = 2.50 * R

Setting the total cost of Option B less than the total cost of Option A, we get:

2.50 * R < 30 + 1 * R

Simplifying this inequality, we get:

1.50 * R < 30

To find the minimum number of rides (R) that satisfies this inequality, we divide both sides of the inequality by 1.50:

R < 20

Therefore, Option B will be more cost-effective than Option A when the number of rides (R) is less than 20.