Dana, Xandra and Gwen had 675 cards. Xandra won some of the cards from Dana and as a result, Xandra's cards increased by 50%. Gwen then won some cards from Xandra and Gwen's cards increased by 80%. Finally, Gwen lost some of her cards to Dana and Dana's cards increased by 25%. In the end, they realised that they each had an equal number of cards. How many percent less did Dana have in the end than what she had at first? Correct your answer to 1 decimal place.

Dana	Xandra	Gwen
675
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 4 p	+ 4 p
		9 p
4 boxes
+ 1 box		- 1 box
5 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
80% = ⁸⁰₁₀₀ = ⁴₅
25% = ²⁵₁₀₀ = ¹₄

Working backwards.

3 groups = 675

1 group = 675 ÷ 3 = 225

1 group = 5 boxes
5 boxes = 225

1 box = 225 ÷ 5 = 45

1 group + 1 box = 9 p
225 + 45 = 9 p
9 p = 270

1 p = 270 ÷ 9 = 30

4 p = 4 x 30 = 120

1 group + 4 p = 3 u
225 + 120 = 3 u
3 u = 345

1 u = 345 ÷ 3 = 115

Number of cards that Dana had at first
= 4 boxes + 1 u
= (4 x 45) + 115
= 180 + 115
= 295

Percent that Dana had less in the end than at first
= ^{295 - 225}₂₉₅ x 100%
≈ 23.7%

Answer(s): 23.7%