The bus fare in a city is \( \$ 1.50 \). People who use the bus have the option of purchasing a monthly coupon book for \( \$ 25.00 \). 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.

To determine the number of times (\( n \)) the bus must be used in a month so that the total monthly cost without the coupon book is the same as with the coupon book, we can set up the following equation: **Without the Coupon Book:** - Cost per ride: \$1.50 - Total monthly cost: \( 1.50n \) **With the Coupon Book:** - Cost of the coupon book: \$25.00 - Reduced cost per ride: \$0.50 - Total monthly cost: \( 25 + 0.50n \) Set the two total costs equal to each other: \[ 1.50n = 25 + 0.50n \] Subtract \( 0.50n \) from both sides to isolate \( n \): \[ 1.50n - 0.50n = 25 \] \[ 1.00n = 25 \] Divide both sides by 1.00: \[ n = 25 \] **Answer:** The bus must be used **25** times.