Xuan, Tina and Shannon had 1080 marbles. Tina won some of the marbles from Xuan and as a result, Tina's marbles increased by 25%. Shannon then won some marbles from Tina and Shannon's marbles increased by 50%. Finally, Shannon 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	Tina	Shannon
1080
	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 = 1080

1 group = 1080 ÷ 3 = 360

1 group = 6 boxes
6 boxes = 360

1 box = 360 ÷ 6 = 60

1 group + 1 box = 3 p
360 + 60 = 3 p
3 p = 420

1 p = 420 ÷ 3 = 140

1 p = 1 x 140 = 140

1 group + 1 p = 5 u
360 + 140 = 5 u
5 u = 500

1 u = 500 ÷ 5 = 100

Number of marbles that Xuan had at first
= 5 boxes + 1 u
= (5 x 60) + 100
= 300 + 100
= 400

Percent that Xuan had less in the end than at first
= ^{400 - 360}₄₀₀ x 100%
≈ 10.0%

Answer(s): 10.0%