Question

The County Fair has to 2 ticket options.Option 1 has an entry fee of $5 and charges $0.65 per ride per ride. Option 2 has an entry fee of $10 and charges $0.45 per ride.How many tickets would have to be purchased for the total cost of option one and option two to be the same.

Answer 1

For 25 tickets total cost of option one and option two to be the same.

Step-by-step explanation:

Let us assume the total number of rides = m

for which BOTH options cost same.

Case: 1

The cost of entry fee  = $5

The cost per ride = $0.65

So, the cost of m rides  = m x ( Cost of 1 ride )  

=  m x ($0.65 ) = 0.65 m

Cost of purchasing m tickets in first ride  = Entry Fee + Per ticket cost

                                                                       = 5 +0.65 m    ..... (1)

Case: 2

The cost of entry fee  = $10

The cost per ride = $0.45

So, the cost of m rides  = m x ( Cost of 1 ride )  

=  m x ($0.45 ) = 0.45 m

Cost of purchasing m tickets in second ride  = Entry Fee + Per ticket cost

                                                                       = 10 +0.45 m    ..... (2)

Now, equating (1) and (2), we get:

5 +0.65 m = 10 +0.45 m

or, 0.20 m = 5

or, m = 5/0.20  = 25

or, m = 25

Hence, for 25 tickets total cost of option one and option two to be the same.