You are a student who plans to attend the amusement park for two days. This will be fun! Now it's time to figure out the cost. You won a coupon for 50% off a 1-day pass but it cannot be combined with other offers. The amusement park also offers a $5 student discount; however, you cannot get the $5 student discount off the 2-day pass. Use the information below to determine which option is the better deal.

• Option 1: Buying a ticket at 50% off today and then purchasing a new 1-day ticket at the student price tomorrow.
• Option 2: Buying a 2-day pass and not using the coupon at all.
Which option would you choose? Please show all your work and explain your answer.

To determine which option is the better deal, we will calculate the cost for each option.

Option 1:
1-day ticket at 50% off: Let's assume the original price of the 1-day ticket is X.
So, the discounted price for the 1-day ticket today would be 0.5X.
1-day ticket at student price tomorrow: Let's assume the student price for a 1-day ticket is Y.
Therefore, the total cost of Option 1 would be 0.5X + Y.

Option 2:
2-day pass price: Let's assume the price of a 2-day pass is Z.

Now, let's compare the two options.
Option 1: 0.5X + Y
Option 2: Z

To determine which option is better, we need to compare the total costs of each option.

However, we don't have the actual values for X, Y, and Z, so we cannot perform the calculation to determine the better deal without specific prices.

To determine which option is the better deal, let's calculate the cost for both options:

Option 1:
- The 1-day pass with a 50% off coupon today:
Let's assume the regular price of a 1-day pass is $X.
With the 50% off coupon, the discounted price of the 1-day pass today would be 50% of X, which is 0.5X.
However, as specified, this coupon cannot be combined with other offers, so we cannot apply the $5 student discount to this ticket.

- The 1-day pass with a student discount tomorrow:
The regular price of a 1-day pass is still $X.
With the $5 student discount, the discounted price of the 1-day pass tomorrow would be X - $5.

Total cost for Option 1: 0.5X + (X - $5)

Option 2:
- The 2-day pass without using the coupon:
Let's assume the regular price of a 2-day pass is $Y.
As specified, we cannot use the 50% off coupon for the 2-day pass, so we need to consider the regular price.

Total cost for Option 2: 2Y

To determine which option is the better deal, compare the total cost for Option 1 to the total cost for Option 2.

If 0.5X + (X - $5) < 2Y, then Option 1 is the better deal.
If 0.5X + (X - $5) > 2Y, then Option 2 is the better deal.
If 0.5X + (X - $5) = 2Y, then both options have the same cost.

By comparing the two options, you can plug in values for X and Y, based on the specific prices set by the amusement park, to determine which option is the better deal for you.