<Question>
One ticket to a show costs $\$20$ at full price. Susan buys $4$ tickets using a coupon that gives her a $25\%$ discount. Pam buys $5$ tickets using a coupon that gives her a $30\%$ discount. How many more dollars does Pam pay than Susan?
</Question>

<think>
<Plan_1>
Okay, let me try to figure out this problem step by step. So, the question is about Susan and Pam buying tickets to a show. Each ticket normally costs $20. Susan buys 4 tickets with a 25% discount, and Pam buys 5 tickets with a 30% discount. We need to find out how many more dollars Pam pays than Susan.

First, I need to understand what exactly is being asked here. It's the difference in the total amount paid by Pam and Susan. So, I need to calculate the total amount each of them paid and then subtract Susan's total from Pam's total to find the difference.
Got that.

Let me start with Susan. She buys 4 tickets with a 25% discount. The original price per ticket is $20. A 25% discount means she pays 75% of the original price, right?

<prompt_1.1> Calculate the total amount Susan pays for her 4 tickets after applying her 25% discount. </prompt_1.1>

Now, moving on to Pam. She buys 5 tickets with a 30% discount. Again, the original price per ticket is $20. A 30% discount means she pays 70% of the original price.
Let me compute that. 70% of $20 is 0.7 * 20 = $14 per ticket. Then, Pam buys 5 tickets, so 5 * $14 = $70. So Pam's total is $70.
-----

Wait, Susan pays $60 and Pam pays $70. The difference is $10. So Pam pays $10 more than Susan.
That seems straightforward. But let me check again to make sure I didn't make any mistakes.

Wait, maybe I should verify the discounts again. For Susan, 25% off on each ticket. So each ticket is $20 - 25% of $20. 25% of 20 is 5, so $20 - $5 = $15 per ticket.
Four tickets would be 4 * 15 = $60. Yep, that's correct.

For Pam, 30% off each ticket. 30% of $20 is 6, so each ticket is $20 - $6 = $14.
Five tickets would be 5 * 14 = $70. That's correct. Then, $70 - $60 = $10.

But wait, let me think again. The problem says "how many more dollars does Pam pay than Susan"? So it's Pam's total minus Susan's total.
Which is 70 - 60 = 10. So the answer is $10.

Alternatively, maybe there's another way to approach this. Let's compute the total discount for each person and subtract that from the total cost without discount.

<prompt_1.2> Verify the solution by calculating the total discount for each person and subtracting it from the total cost without discount. </prompt_1.2>
-----

But just to make sure, let's consider if there's any possibility of a different interpretation. For example, maybe the coupons are applied to the total amount instead of per ticket. Let me check that.

<prompt_1.3> Consider alternative interpretations of the coupon application and confirm the correct interpretation. </prompt_1.3>

Another point to consider: Is there any tax or additional fees mentioned? The problem states the ticket costs $20 at full price, and the coupons give discounts. There's no mention of taxes or other charges, so we can assume the total is just the discounted price of the tickets.

<prompt_1.4> Perform a final verification of the calculations and confirm the correctness of the solution. </prompt_1.4>

Alternatively, if we compute the difference per ticket, but that might complicate things. Let's see.

<prompt_1.5> Explore alternative methods to confirm the solution and ensure consistency in the results. </prompt_1.5>
</Plan_1>

<Execution_1>
<execution_1.1>
Let me confirm that. If something has a 25% discount, you subtract 25% from 100%, so 75% remains. Yes, that's right. So each ticket for Susan is $20 * 0.75. Let me calculate that: 20 * 0.75 = $15. So each ticket costs Susan $15. Since she buys 4 tickets, the total cost for Susan is 4 * $15.
</execution_1.1>

<execution_1.2>
Without any discount, Susan would pay 4 * 20 = $80, and Pam would pay 5 * 20 = $100. Then, applying their discounts.

Susan's discount is 25% on each ticket, which we already calculated. Alternatively, total discount for Susan is 25% of $80. 25% of 80 is 20, so she pays $80 - $20 = $60. That's the same as before.

For Pam, if the discount is applied to the total, it would be 30% of $100, which is $30. So Pam pays $100 - $30 = $70. Again, same result.

Therefore, the difference is still $70 - $60 = $10.
</execution_1.2>

<execution_1.3>
If the discount was applied to the total, then for Susan, 4 tickets at $20 each is $80. A 25% discount on $80 would be $80 * 0.25 = $20 discount. So she pays $80 - $20 = $60. That's the same as before. For Pam, 5 tickets at $20 is $100. 30% discount is $100 * 0.30 = $30 discount. So she pays $100 - $30 = $70. Again, the same result. So the difference is still $10. So whether the discount is per ticket or on the total, in this case, the result is the same because the discount is applied to the total amount either way.
</execution_1.3>

<execution_1.4>
So, we can proceed with the original calculation.

Another way to check: Let's compute the total without discount for each. Susan would pay 4*20 = 80. With 25% discount, so 80 * 0.25 = 20 discount. 80 - 20 = 60. Similarly, Pam's total without discount is 5*20 = 100. 30% discount is 100 * 0.30 = 30. 100 - 30 = 70. Then, 70 - 60 = 10.
</execution_1.4>

<execution_1.5>
Susan's discount per ticket is 25%, so $5 off per ticket. Pam's discount is 30%, so $6 off per ticket. But they buy different numbers of tickets. So, the difference per ticket is $1, but since Pam buys more tickets, the total difference would be more than just one extra ticket. Let's see: Pam buys 5 tickets, Susan buys 4. So, one extra ticket at the discounted rate. But Pam's discount is 30%, which is $6 off per ticket, but Susan's discount is 25%, which is $5 off per ticket. So, the difference per ticket is $1. But Pam buys one more ticket. However, the discounts are applied per ticket, so the extra $1 per ticket would apply to the extra ticket Pam buys. So, 5 extra dollars for that one ticket. But wait, Susan's total is 4 tickets at $15 each, Pam's is 5 tickets at $14 each. So, the fifth ticket for Pam is $14, while Susan didn't buy that ticket. So, the difference would be $14 (Pam's fifth ticket) compared to Susan's fourth ticket at $15. So, the difference for that one ticket is $1. Since Pam buys one more ticket, that's an extra $1. Then, for the first four tickets, both bought four tickets, so the difference would be the per-ticket difference times four.
</execution_1.5>
</Execution_1>

<Plan_2>
Based on execution_1.1:
Let me compute that: 5 * 14 = 70.
Therefore, Pam pays $70.

Now, the question is asking how many more dollars Pam pays than Susan. So, we need to subtract Susan's total from Pam's total.
That would be $70 - $60 = $10. So, Pam pays $10 more than Susan.

Wait a second, let me double-check my calculations to make sure I didn't make any errors.

<prompt_2.1> Verify the calculations for the total amounts paid by Susan and Pam. </prompt_2.1>
</Plan_2>

<Execution_2>
<execution_2.1>
For Susan: 4 tickets at $15 each. 4*15 is 60. Yes, that's right. For Pam: 5 tickets at $14 each. 5*14 is 70. Correct. Then, 70 - 60 is 10. So, the difference is $10.
</execution_2.1>
</Execution_2>

<Plan_3>
Based on execution_2.1:
But just to ensure that there isn't any trick in the problem, like the coupons being combined or something else.

<prompt_3.1> Ensure there is no trick in the problem, such as coupons being combined or applied differently. </prompt_3.1>
</Plan_3>

<Execution_3>
<execution_3.1>
The problem states that Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickets using a coupon that gives her a 30% discount. It doesn't mention any limitations on the coupons, like needing to buy a certain number of tickets or any maximum discount. So, the discount is applied per ticket, and the total is calculated accordingly. Therefore, the calculations should be as we did.
</execution_3.1>
</Execution_3>

<Final_answer>
Therefore, Pam pays $\boxed{10}$ dollars more than Susan.
</Final_answer>
</think>