Pamela, Diana and Kathy had 1224 cards. Diana won some of the cards from Pamela and as a result, Diana's cards increased by 50%. Kathy then won some cards from Diana and Kathy's cards increased by 75%. Finally, Kathy lost some of her cards to Pamela and Pamela's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Pamela have in the end than what she had at first? Correct your answer to 1 decimal place.

Pamela	Diana	Kathy
1224
	2 u
- 1 u	+ 1 u
	3 u
		4 p
	- 3 p	+ 3 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
75% = ⁷⁵₁₀₀ = ³₄
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1224

1 group = 1224 ÷ 3 = 408

1 group = 6 boxes
6 boxes = 408

1 box = 408 ÷ 6 = 68

1 group + 1 box = 7 p
408 + 68 = 7 p
7 p = 476

1 p = 476 ÷ 7 = 68

3 p = 3 x 68 = 204

1 group + 3 p = 3 u
408 + 204 = 3 u
3 u = 612

1 u = 612 ÷ 3 = 204

Number of cards that Pamela had at first
= 5 boxes + 1 u
= (5 x 68) + 204
= 340 + 204
= 544

Percent that Pamela had less in the end than at first
= ^{544 - 408}₅₄₄ x 100%
≈ 25.0%

Answer(s): 25.0%