Fiona, Jade and Penelope had 612 buttons. Jade won some of the buttons from Fiona and as a result, Jade's buttons increased by 50%. Penelope then won some buttons from Jade and Penelope's buttons increased by 75%. Finally, Penelope lost some of her buttons to Fiona and Fiona's buttons increased by 20%. In the end, they realised that they each had an equal number of buttons. How many percent less did Fiona have in the end than what she had at first? Correct your answer to 1 decimal place.

Fiona	Jade	Penelope
612
	2 u
- 1 u	+ 1 u
	3 u
		4 p
	- 3 p	+ 3 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
75% = ⁷⁵₁₀₀ = ³₄
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 612

1 group = 612 ÷ 3 = 204

1 group = 6 boxes
6 boxes = 204

1 box = 204 ÷ 6 = 34

1 group + 1 box = 7 p
204 + 34 = 7 p
7 p = 238

1 p = 238 ÷ 7 = 34

3 p = 3 x 34 = 102

1 group + 3 p = 3 u
204 + 102 = 3 u
3 u = 306

1 u = 306 ÷ 3 = 102

Number of buttons that Fiona had at first
= 5 boxes + 1 u
= (5 x 34) + 102
= 170 + 102
= 272

Percent that Fiona had less in the end than at first
= ^{272 - 204}₂₇₂ x 100%
≈ 25.0%

Answer(s): 25.0%