A train ticket in a certain city is $2.00. People who use the train also have the option of puchasing a frequent rider pass for $17.25 each month. With the pass, each ticket costs only $1.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the total monthly cost with the pass.

Question

A train ticket in a certain city is $2.00. People who use the train also have the option of puchasing a frequent rider pass for $17.25 each month. With the pass, each ticket costs only $1.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the total monthly cost with the pass.

Answer 1

Without the pass, the rider pays 2.00 * T

With the pass the rider pays 17.25 + 1.25*T

Set the two equal to each other, and solve for T

2.00 * T = 17.25 + 1.25 * T

where T is the number of tickets

Answer 2

Let's assume the number of times the train must be used in a month is represented by x.

Without the pass:
Cost per ticket = $2.00
Total cost without the pass = $2.00 * x = $2x

With the pass:
Cost per ticket = $1.25
Cost of the pass = $17.25
Total cost with the pass = ($1.25 * x) + $17.25 = $1.25x + $17.25

To find the number of times the train must be used in a month so that the total costs are the same, we can set up an equation:

$2x = $1.25x + $17.25

Now, let's solve for x:

$2x - $1.25x = $17.25
$0.75x = $17.25
x = $17.25 / $0.75
x = 23

Therefore, the train must be used 23 times in a month for the total monthly cost without the pass to be the same as the total monthly cost with the pass.

Answer 3

To determine the number of times the train must be used in a month for the total monthly cost with the pass to be the same as the total monthly cost without the pass, we need to set up an equation.

Let's assume the number of times the train is used in a month is 'x'.

Without the pass:
The cost of each train ticket is $2.00, so the total cost without the pass is 2 * x = 2x.

With the pass:
The cost of the pass is $17.25.
The cost of each train ticket with the pass is $1.25, so the total cost with the pass is 17.25 + 1.25 * x = 17.25 + 1.25x.

To find the number of times the train must be used in a month when the two costs are equal, we can set up the following equation:

2x = 17.25 + 1.25x

Now, let's solve this equation to find the value of 'x' by isolating the terms with 'x' on one side:

2x - 1.25x = 17.25
0.75x = 17.25
x = 17.25 / 0.75

Using a calculator, we can find:

x ≈ 23

Therefore, the train must be used approximately 23 times in a month for the total monthly cost without the pass to be the same as the total monthly cost with the pass.