A standard train ticket in a certain city costs $2.50 per ride. People who use the train also have the option of purchasing a frequent-rider pass for $18.00 each month. With the pass, a ticket costs only$1.75 per ride. How many train rides in a month make the frequent-rider pass a better deal than standard train tickets?

Question

A standard train ticket in a certain city costs $2.50 per ride. People who use the train also have the option of purchasing a frequent-rider pass for $18.00 each month. With the pass, a ticket costs only$1.75 per ride. How many train rides in a month make the frequent-rider pass a better deal than standard train tickets?

Answer 1

2.50 n = 1.75 n + 18

.75 n = 18

n = 18/.75

Answer 2

To determine how many train rides in a month make the frequent-rider pass a better deal than standard train tickets, we can set up an equation.

Let x be the number of train rides per month.

For standard train tickets:
Cost per ride = $2.50
Total cost for x rides = $2.50 * x

For frequent-rider pass:
Cost per ride = $1.75
Pass cost = $18.00
Total cost for x rides = Pass cost + (Cost per ride * x) = $18.00 + ($1.75 * x)

We need to find the point where the total cost for x rides using the frequent-rider pass is less than the total cost for x rides using standard train tickets.

So, we can set up the inequality:

$18.00 + ($1.75 * x) < $2.50 * x

Simplifying the inequality:

18 + 1.75x < 2.50x

Rearranging the inequality:

18 < 2.50x - 1.75x

18 < 0.75x

Dividing both sides by 0.75:

x > 18 / 0.75

x > 24

Therefore, if the number of train rides in a month is greater than 24, the frequent-rider pass becomes a better deal than standard train tickets.

Answer 3

To determine how many train rides in a month make the frequent-rider pass a better deal than standard train tickets, we need to compare the costs of using the pass versus using standard tickets.

Let's assume the number of train rides in a month is represented by 'x'.

Using standard train tickets:
The cost of each ride is $2.50.
So the total cost for 'x' rides using standard tickets would be 2.50 * x = 2.50x.

Using the frequent-rider pass:
The cost of the pass is $18.00 per month, regardless of the number of rides.
The cost of each ride with the pass is $1.75.
So the total cost for 'x' rides using the pass would be 18.00 + 1.75 * x = 18.00 + 1.75x.

To find the point at which the pass is a better deal, we set up an inequality:
2.50x > 18.00 + 1.75x

Now, we can simplify the inequality and solve for 'x':
2.50x - 1.75x > 18.00
0.75x > 18.00
x > 18.00 / 0.75
x > 24

Hence, if you take more than 24 train rides in a month, the frequent-rider pass becomes a better deal than using standard train tickets.