Pamela, Mary and Xylia had 864 buttons. Mary won some of the buttons from Pamela and as a result, Mary's buttons increased by 50%. Xylia then won some buttons from Mary and Xylia's buttons increased by 40%. Finally, Xylia lost some of her buttons to Pamela and Pamela's buttons increased by 20%. In the end, they realised that they each had an equal number of buttons. How many percent less did Pamela have in the end than what she had at first? Correct your answer to 1 decimal place.

Pamela	Mary	Xylia
864
	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 = 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

2 p = 2 x 48 = 96

1 group + 2 p = 3 u
288 + 96 = 3 u
3 u = 384

1 u = 384 ÷ 3 = 128

Number of buttons that Pamela had at first
= 5 boxes + 1 u
= (5 x 48) + 128
= 240 + 128
= 368

Percent that Pamela had less in the end than at first
= ^{368 - 288}₃₆₈ x 100%
≈ 21.7%

Answer(s): 21.7%