Data Sufficiency

Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park. She received 30% off the adult tickets and 15% off the child and senior tickets. Was the total amount of the 4 discounts greater than 20% of the sum of the regular prices of the 4 tickets?

(1) The original price of an adult ticket was $48, the original price of the senior ticket was $24, and the original price of the child ticket was less than the senior ticket.
(2) The original price of the child ticket was $12.

The OA is A.

Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park. She received 30% off the adult tickets and 15% off the child and senior tickets. Was the total amount of the 4 discounts greater than 20% of the sum of the regular prices of the 4 tickets?

1. The original price of an adult ticket was $48, the original price of the senior ticket was $24, and the original price of the child ticket was less than the senior ticket.

2. The original price of the child ticket was $12.

Statement 1: The original price of an adult ticket was $48, the original price of the senior ticket was $24, and the original price of the child ticket was less than the senior ticket.
Test EXTREMES.

Case 1: Test the THRESHOLD price for the original price of the child ticket.
Since the original price of the child ticket must be less than the original price of the senior ticket, the threshold price for the child ticket = 24.
In this case:
(sum of the discounts)/(sum of the original prices) = (.3*2*48 + .15*24 + .15*24)/(2*48 + 24 + 24) = (28.8 + 3.6 + 3.6)/144 = 36/144 = 25%.

Case 2: Test a very small value for the original price of the child ticket.
Let the original price of a child ticket = 1 cent.
Here, the original price and the discounted price of the child ticket will both be so small that they can be disregarded in our calculations.
In this case:
(sum of the other discounts)/(sum of the other original prices) = (.3*2*48 + .15*24)/(2*48 + 24) = (28.8 + 3.6)/120 ≈ 32/120 = 26.66%.

Since the discount is greater than 20% in each case, SUFFICIENT.

Statement 2: The original price of the child ticket was $12.
No way to determine whether the sum of the discounts was greater than 20%.
INSUFFICIENT.

The correct answer is A.

Alternate approach:

Alternate approach:

Let A = the regular price of an adult ticket, C = the regular price of a child ticket, and S = the regular price of a senior ticket.

Was the total amount of the 4 discounts greater than 20% of the sum of the regular prices of the 4 tickets?
More specifically:
Is (30% of 2A) + (15% of C) + (15% of S) > 20% of (2A + C + S)?

Or:
(30)(2A) + 15C + 15S > 20(2A + C + S) ?
60A + 15C + 15S > 40A + 20C + 20S ?
20A > 5C + 5S ?
4A > C + S ?

Questions stem, rephrased:
Is 4A > C + S?

Statement 1:
Subsituting A=48, S=24 and C<24 into 4A > C + S, we get:
4*48 > (less than 24) + 24 ?
192 > less than 48 ?
YES.
SUFFICIENT.

Statement 2:
No way to determine whether 4A > C + S.
INSUFFICIENT.

The correct answer is A.