Sarah, Fanny and Xylia had 648 cards. Fanny won some of the cards from Sarah and as a result, Fanny's cards increased by 25%. Xylia then won some cards from Fanny and Xylia's cards increased by 50%. Finally, Xylia lost some of her cards to Sarah and Sarah's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Sarah have in the end than what she had at first? Correct your answer to 1 decimal place.

Sarah	Fanny	Xylia
648
	4 u
- 1 u	+ 1 u
	5 u
		2 p
	- 1 p	+ 1 p
		3 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

25% = ²⁵₁₀₀ = ¹₄
50% = ⁵⁰₁₀₀ = ¹₂
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 648

1 group = 648 ÷ 3 = 216

1 group = 6 boxes
6 boxes = 216

1 box = 216 ÷ 6 = 36

1 group + 1 box = 3 p
216 + 36 = 3 p
3 p = 252

1 p = 252 ÷ 3 = 84

1 p = 1 x 84 = 84

1 group + 1 p = 5 u
216 + 84 = 5 u
5 u = 300

1 u = 300 ÷ 5 = 60

Number of cards that Sarah had at first
= 5 boxes + 1 u
= (5 x 36) + 60
= 180 + 60
= 240

Percent that Sarah had less in the end than at first
= ^{240 - 216}₂₄₀ x 100%
≈ 10.0%

Answer(s): 10.0%