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.

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.