Nora, Roshel and Irene had 1350 buttons. Roshel won some of the buttons from Nora and as a result, Roshel's buttons increased by 20%. Irene then won some buttons from Roshel and Irene's buttons increased by 50%. Finally, Irene lost some of her buttons to Nora and Nora's buttons increased by 25%. In the end, they realised that they each had an equal number of buttons. How many percent less did Nora have in the end than what she had at first? Correct your answer to 1 decimal place.

Nora	Roshel	Irene
1350
	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 = 1350

1 group = 1350 ÷ 3 = 450

1 group = 5 boxes
5 boxes = 450

1 box = 450 ÷ 5 = 90

1 group + 1 box = 3 p
450 + 90 = 3 p
3 p = 540

1 p = 540 ÷ 3 = 180

1 p = 1 x 180 = 180

1 group + 1 p = 6 u
450 + 180 = 6 u
6 u = 630

1 u = 630 ÷ 6 = 105

Number of buttons that Nora had at first
= 4 boxes + 1 u
= (4 x 90) + 105
= 360 + 105
= 465

Percent that Nora had less in the end than at first
= ^{465 - 450}₄₆₅ x 100%
≈ 3.2%

Answer(s): 3.2%