Julie, Hilda and Eva had 864 cards. Hilda won some of the cards from Julie and as a result, Hilda's cards increased by 25%. Eva then won some cards from Hilda and Eva's cards increased by 50%. Finally, Eva lost some of her cards to Julie and Julie's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Julie have in the end than what she had at first? Correct your answer to 1 decimal place.

Julie	Hilda	Eva
864
	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 = 864

1 group = 864 ÷ 3 = 288

1 group = 6 boxes
6 boxes = 288

1 box = 288 ÷ 6 = 48

1 group + 1 box = 3 p
288 + 48 = 3 p
3 p = 336

1 p = 336 ÷ 3 = 112

1 p = 1 x 112 = 112

1 group + 1 p = 5 u
288 + 112 = 5 u
5 u = 400

1 u = 400 ÷ 5 = 80

Number of cards that Julie had at first
= 5 boxes + 1 u
= (5 x 48) + 80
= 240 + 80
= 320

Percent that Julie had less in the end than at first
= ^{320 - 288}₃₂₀ x 100%
≈ 10.0%

Answer(s): 10.0%