Dana, Nicole and Xandra had 936 erasers. Nicole won some of the erasers from Dana and as a result, Nicole's erasers increased by 50%. Xandra then won some erasers from Nicole and Xandra's erasers increased by 30%. Finally, Xandra lost some of her erasers to Dana and Dana's erasers increased by 20%. In the end, they realised that they each had an equal number of erasers. How many percent less did Dana have in the end than what she had at first? Correct your answer to 1 decimal place.

Dana	Nicole	Xandra
936
	2 u
- 1 u	+ 1 u
	3 u
		10 p
	- 3 p	+ 3 p
		13 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
30% = ³⁰₁₀₀ = ³₁₀
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 936

1 group = 936 ÷ 3 = 312

1 group = 6 boxes
6 boxes = 312

1 box = 312 ÷ 6 = 52

1 group + 1 box = 13 p
312 + 52 = 13 p
13 p = 364

1 p = 364 ÷ 13 = 28

3 p = 3 x 28 = 84

1 group + 3 p = 3 u
312 + 84 = 3 u
3 u = 396

1 u = 396 ÷ 3 = 132

Number of erasers that Dana had at first
= 5 boxes + 1 u
= (5 x 52) + 132
= 260 + 132
= 392

Percent that Dana had less in the end than at first
= ^{392 - 312}₃₉₂ x 100%
≈ 20.4%

Answer(s): 20.4%