Esther, Eva and Diana had 1170 buttons. Eva won some of the buttons from Esther and as a result, Eva's buttons increased by 20%. Diana then won some buttons from Eva and Diana's buttons increased by 50%. Finally, Diana lost some of her buttons to Esther and Esther's buttons increased by 25%. In the end, they realised that they each had an equal number of buttons. How many percent less did Esther have in the end than what she had at first? Correct your answer to 1 decimal place.

Esther	Eva	Diana
1170
	5 u
- 1 u	+ 1 u
	6 u
		2 p
	- 1 p	+ 1 p
		3 p
4 boxes
+ 1 box		- 1 box
5 boxes
1 group	1 group	1 group

20% = ²⁰₁₀₀ = ¹₅
50% = ⁵⁰₁₀₀ = ¹₂
25% = ²⁵₁₀₀ = ¹₄

Working backwards.

3 groups = 1170

1 group = 1170 ÷ 3 = 390

1 group = 5 boxes
5 boxes = 390

1 box = 390 ÷ 5 = 78

1 group + 1 box = 3 p
390 + 78 = 3 p
3 p = 468

1 p = 468 ÷ 3 = 156

1 p = 1 x 156 = 156

1 group + 1 p = 6 u
390 + 156 = 6 u
6 u = 546

1 u = 546 ÷ 6 = 91

Number of buttons that Esther had at first
= 4 boxes + 1 u
= (4 x 78) + 91
= 312 + 91
= 403

Percent that Esther had less in the end than at first
= ^{403 - 390}₄₀₃ x 100%
≈ 3.2%

Answer(s): 3.2%