Usha, Victoria and Joelle had 720 buttons. Victoria won some of the buttons from Usha and as a result, Victoria's buttons increased by 20%. Joelle then won some buttons from Victoria and Joelle's buttons increased by 60%. Finally, Joelle lost some of her buttons to Usha and Usha's buttons increased by 25%. In the end, they realised that they each had an equal number of buttons. How many percent less did Usha have in the end than what she had at first? Correct your answer to 1 decimal place.

Usha	Victoria	Joelle
720
	5 u
- 1 u	+ 1 u
	6 u
		5 p
	- 3 p	+ 3 p
		8 p
4 boxes
+ 1 box		- 1 box
5 boxes
1 group	1 group	1 group

20% = ²⁰₁₀₀ = ¹₅
60% = ⁶⁰₁₀₀ = ³₅
25% = ²⁵₁₀₀ = ¹₄

Working backwards.

3 groups = 720

1 group = 720 ÷ 3 = 240

1 group = 5 boxes
5 boxes = 240

1 box = 240 ÷ 5 = 48

1 group + 1 box = 8 p
240 + 48 = 8 p
8 p = 288

1 p = 288 ÷ 8 = 36

3 p = 3 x 36 = 108

1 group + 3 p = 6 u
240 + 108 = 6 u
6 u = 348

1 u = 348 ÷ 6 = 58

Number of buttons that Usha had at first
= 4 boxes + 1 u
= (4 x 48) + 58
= 192 + 58
= 250

Percent that Usha had less in the end than at first
= ^{250 - 240}₂₅₀ x 100%
≈ 4.0%

Answer(s): 4.0%