The bus fare in a city is $1.50 People who use the bus have the option of purchasing a monthly coupon book for $30.00 With the coupon book, the fare is reduced to 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.

Step-by-step explanation:

let x be the number of rides

y is the total cost

the model for cost for people who use coupon is given as

y=1.5x+301

for people without coupon

y= 50x2

equating 1 and 2 we can find x

50x=1.5x+30

collect like terms

50-1.5x=30

-1.5x=30-50

-1.5x=-20

x=20/1.5

x=13.33

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 is 13.33