The bus fare in a city is $2.00. People who use the bus have the option of purchasing a monthly coupon book for $ 20.00. With the coupon book, the fare is reduced to $1.00. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.

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The bus fare in a city is $2.00. People who use the bus have the option of purchasing a monthly coupon book for $ 23.00. With the coupon book, the fare is reduced to $1.00. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book

Let's break down the problem step-by-step to find the number of times the bus must be used in a month for the total monthly cost without the coupon book to be the same as the total monthly cost with the coupon book.

Step 1: Calculate the total monthly cost without the coupon book.
The bus fare without the coupon book is $2.00. So, the total monthly cost without the coupon book will be 2 times the number of bus rides in a month. Let's represent the number of bus rides in a month as "x".

Total monthly cost without coupon book = $2.00 * x

Step 2: Calculate the total monthly cost with the coupon book.
With the coupon book, the fare is reduced to $1.00 per ride. So, the total monthly cost with the coupon book will be 1 times the number of bus rides in a month, which is also represented by "x".

Total monthly cost with coupon book = $1.00 * x

Step 3: Equate the two total monthly costs to find the number of times the bus must be used.
Since we want the total monthly cost without the coupon book to be the same as the total monthly cost with the coupon book, we can set up the equation:

$2.00 * x = $1.00 * x

Step 4: Solve for x.
To solve the equation, we can cancel out the common factor of "x" on both sides:

2 * x = 1 * x

This simplifies to:

2 = 1

Since the equation is not true, it means there is no solution. In other words, there is no number of bus rides in a month that will make the total monthly cost without the coupon book the same as the total monthly cost with the coupon book.

Thus, the bus can never be used a specific number of times in a month for the total monthly cost without the coupon book to be the same as the total monthly cost with the coupon book.

To determine the number of times the bus must be used in a month so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book, we need to set up an equation.

Let's call the number of times the bus is used in a month "x".

Without the coupon book, the total monthly cost for x number of bus rides is calculated by multiplying the bus fare ($2.00) by the number of rides, which gives us 2x.

With the coupon book, the total monthly cost for x number of bus rides is determined by adding the cost of the coupon book ($20.00) to the reduced fare ($1.00) multiplied by the number of rides. This gives us 20 + 1x.

To find the number of times the bus must be used in a month for both costs to be the same, we set up the equation:

2x = 20 + x

Now, let's solve for x:

2x - x = 20

x = 20

Therefore, the bus must be used 20 times in a month for the total monthly cost without the coupon book to be the same as the total monthly cost with the coupon book.

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