The bus fare in a city is $1.75. People who use the bus have the options of purchasing a monthly coupon for $29.00. With the coupon book, the fare is reduced to $0.75. 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...i think its 29 but can you double check it please? thanks
Sort of, if the person used the bus only once a day. But normally, one uses the bus on the trip going to the city, then again back, or twice a day.
You are right, the person saves 1 dollar per trip. The question is how many trips a day the person takes.
Anyway, it takes 29 trips to break even.
To determine 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, we can set up an equation.
Let's assume the number of times the bus is used in a month is 'x'.
Without the coupon book:
Cost per bus ride = $1.75
Total monthly cost without coupon book = Cost per bus ride x Number of times the bus is used
= $1.75x
With the coupon book:
Cost per bus ride = $0.75
Total monthly cost with coupon book = Cost per bus ride x Number of times the bus is used
= $0.75x
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:
$1.75x = $0.75x
To solve for 'x', we can subtract $0.75x from both sides of the equation:
$1.75x - $0.75x = $0.75x - $0.75x
$1x = $0
This means the equation is satisfied for any value of 'x'. Therefore, there is no specific 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.
So, the answer is not 29.
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.