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 assume the number of times the bus is used in a month is "n".
Without the coupon book, the cost of taking the bus n times in a month would be 1.75 * n dollars.
With the coupon book, the cost of taking the bus n times in a month would be 0.75 * n dollars, plus the cost of purchasing the coupon book, which is a one-time fee of $29.00.
So we can set up the equation:
1.75 * n = 0.75 * n + 29.00
To solve for n, we can first subtract 0.75n from both sides of the equation:
1.75n - 0.75n = 29.00
This simplifies to:
1.00n = 29.00
Dividing both sides of the equation by 1.00:
n = 29.00
So, 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 is 29 times.
Therefore, your initial guess of 29 is correct.