Question 1.
They usually charge $7 per day to swim at the pool. The offer consist of: Paying an enrollment fee is $30 and then $4 per day.
It means that by enrolling you save 3$ per day. If you save $3 per day, in 10 days you would be saving $30 dollars which is the enrollment fee. This can be calculated by applying the rule of three:
If I save $3 -------------> 1 day?
$30 ----------> How many days?
Days = ($30 * 1day)/$3 = 10 days.
Then, after 10 days, the offer becomes a better deal.
Question 2.
I only have $60 to spend the rest of the summer. Which offer would be the best value?
NOT paying the enrollment fee would be the best value. The reason is the following:
If I pay the enrollment fee, I spend $30. So I just have $30 remaining. Then, paying $4 a day, it means that I could just pay 7 daily passes, it means that I could go to the pool just seven days.
If I don't pay the enrollment fee, I would have the entire $60 dollars to buy daily passes. The price of each pass would be $7, so $60/7 = 8.5. It means that I could go just 8 days to the pool. One day more than the other option.
So if I only have $60, the best option is NOT to pay the enrollment fee.
Question 3.
If the swim center decides to change the the enrollment fee to $23 and then paying just $4 per daily pass. Then:
If I have only $60 dollars, after paying the enrollment fee I will only have $37.
If each daily pass costs $4, then I will be able to buy $37/$4 = 9.25 = 9 daily passes.
So, if the swim center decides to change the enrollment fee to $23, the the best option is paying the enrollment fee.