Yen, Xuan and Victoria had 1080 buttons. Xuan won some of the buttons from Yen and as a result, Xuan's buttons increased by 25%. Victoria then won some buttons from Xuan and Victoria's buttons increased by 40%. Finally, Victoria lost some of her buttons to Yen and Yen's buttons increased by 20%. In the end, they realised that they each had an equal number of buttons. How many percent less did Yen have in the end than what she had at first? Correct your answer to 1 decimal place.

Yen	Xuan	Victoria
1080
	4 u
- 1 u	+ 1 u
	5 u
		5 p
	- 2 p	+ 2 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

25% = ²⁵₁₀₀ = ¹₄
40% = ⁴⁰₁₀₀ = ²₅
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 = 7 p
360 + 60 = 7 p
7 p = 420

1 p = 420 ÷ 7 = 60

2 p = 2 x 60 = 120

1 group + 2 p = 5 u
360 + 120 = 5 u
5 u = 480

1 u = 480 ÷ 5 = 96

Number of buttons that Yen had at first
= 5 boxes + 1 u
= (5 x 60) + 96
= 300 + 96
= 396

Percent that Yen had less in the end than at first
= ^{396 - 360}₃₉₆ x 100%
≈ 9.1%

Answer(s): 9.1%