The bus fare in a city is $2.00. People who use the bus have the option of purchasing a monthly coupon book for $24.00. 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
24+n = 2n
To 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, we need to set up an equation.
Let's assume the number of times the bus is used in a month is 'x'.
Without the coupon book, the total monthly cost would be $2.00 multiplied by 'x', since each bus ride costs $2.00.
So, the total monthly cost without the coupon book is 2x dollars.
With the coupon book, the fare is reduced to $1.00. So, the total monthly cost with the coupon book would be $1.00 multiplied by 'x'.
The total monthly cost with the coupon book is 1x dollars.
According to the given information, the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book. This can be represented by the equation:
2x = 1x
To solve this equation, subtract '1x' from both sides of the equation:
2x - 1x = 0
Simplifying the equation:
x = 0
This implies that in order for the total monthly cost without the coupon book to be the same as the total monthly cost with the coupon book, 'x' should be equal to zero.
However, in practical terms, you cannot take zero bus rides in a month to make the costs equal. Therefore, there is no solution for this equation, and it is not possible for the total monthly costs to be the same without using the coupon book.
Let's assume the number of times the bus is used in a month is represented by 'x'.
Without the coupon book:
The cost per ride is $2.00.
So, the total monthly cost without the coupon book is 2 * x = 2x dollars.
With the coupon book:
The cost per ride is $1.00.
So, the total monthly cost with the coupon book is 1 * x = x dollars.
We want to find the number of times 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.
Setting the two equations equal to each other, we have:
2x = x
Simplifying the equation, we get:
x = 0
Since this doesn't make sense in the context of the problem (we can't have used the bus 0 times in a month and still compare costs), it means there isn't a solution where the costs are equal.
Therefore, there is no number of times the bus must be used in a month that would make the total monthly cost without the coupon book the same as the total monthly cost with the coupon book.