Xuan, Penelope and Gem had 864 marbles. Penelope won some of the marbles from Xuan and as a result, Penelope's marbles increased by 50%. Gem then won some marbles from Penelope and Gem's marbles increased by 75%. Finally, Gem lost some of her marbles to Xuan and Xuan's marbles increased by 20%. In the end, they realised that they each had an equal number of marbles. How many percent less did Xuan have in the end than what she had at first? Correct your answer to 1 decimal place.

Xuan	Penelope	Gem
864
	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 = 864

1 group = 864 ÷ 3 = 288

1 group = 6 boxes
6 boxes = 288

1 box = 288 ÷ 6 = 48

1 group + 1 box = 7 p
288 + 48 = 7 p
7 p = 336

1 p = 336 ÷ 7 = 48

3 p = 3 x 48 = 144

1 group + 3 p = 3 u
288 + 144 = 3 u
3 u = 432

1 u = 432 ÷ 3 = 144

Number of marbles that Xuan had at first
= 5 boxes + 1 u
= (5 x 48) + 144
= 240 + 144
= 384

Percent that Xuan had less in the end than at first
= ^{384 - 288}₃₈₄ x 100%
≈ 25.0%

Answer(s): 25.0%