HELP!!!! The bus fare in a city is $1.50. People who use the bus have the option of purchasing a monthly coupon book for $24.00. 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.

Question

anonymous · Answer

Let x = number of bus fares. 
Cost of fares without coupon book = 1.50x
Cost of fares WITH coupon book = .50x + 24 
1.50x = .50x+24
To solve the equation, subtract .50x from each side of the equation:
1.50x -.50x = .50x-.50x + 24
1.00x = 24
x= 24 fares

anonymous · Answer

x = number of times you ride on the bus
y = total cost


without book: y = 1.5x

with book: y = 24 + 0.5x

Using systems of equations (equal values method), set the equations equal to each other

1.5x = 24+0.5x

Solve with algebra

x = 24 times on the bus