Usha, Tammy and Xuan had 1188 buttons. Tammy won some of the buttons from Usha and as a result, Tammy's buttons increased by 50%. Xuan then won some buttons from Tammy and Xuan's buttons increased by 40%. Finally, Xuan lost some of her buttons to Usha and Usha's buttons increased by 20%. 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	Tammy	Xuan
1188
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 2 p	+ 2 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
40% = ⁴⁰₁₀₀ = ²₅
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1188

1 group = 1188 ÷ 3 = 396

1 group = 6 boxes
6 boxes = 396

1 box = 396 ÷ 6 = 66

1 group + 1 box = 7 p
396 + 66 = 7 p
7 p = 462

1 p = 462 ÷ 7 = 66

2 p = 2 x 66 = 132

1 group + 2 p = 3 u
396 + 132 = 3 u
3 u = 528

1 u = 528 ÷ 3 = 176

Number of buttons that Usha had at first
= 5 boxes + 1 u
= (5 x 66) + 176
= 330 + 176
= 506

Percent that Usha had less in the end than at first
= ^{506 - 396}₅₀₆ x 100%
≈ 21.7%

Answer(s): 21.7%