Question

the bus fare in a city is $1.50. people who use the bus have the option of purchasing a monthly coupon book for $26.00. with the coupon book, the fare is reduced to $0.50. 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.
the bus must be used \square times.

Explanation:

Step1: Define variable for bus rides

Let $x$ = number of bus rides in a month.

Step2: Set cost equations equal

Cost without coupon: $1.50x$; Cost with coupon: $26 + 0.50x$. Set equal:
$$1.50x = 26 + 0.50x$$

Step3: Isolate $x$ term

Subtract $0.50x$ from both sides:
$$1.50x - 0.50x = 26$$
$$1.00x = 26$$

Answer:

26