Rachel, Betty and Tiffany had 945 erasers. Betty won some of the erasers from Rachel and as a result, Betty's erasers increased by 50%. Tiffany then won some erasers from Betty and Tiffany's erasers increased by 75%. Finally, Tiffany lost some of her erasers to Rachel and Rachel's erasers increased by 25%. In the end, they realised that they each had an equal number of erasers. How many percent less did Rachel have in the end than what she had at first? Correct your answer to 1 decimal place.

Rachel	Betty	Tiffany
945
	2 u
- 1 u	+ 1 u
	3 u
		4 p
	- 3 p	+ 3 p
		7 p
4 boxes
+ 1 box		- 1 box
5 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
75% = ⁷⁵₁₀₀ = ³₄
25% = ²⁵₁₀₀ = ¹₄

Working backwards.

3 groups = 945

1 group = 945 ÷ 3 = 315

1 group = 5 boxes
5 boxes = 315

1 box = 315 ÷ 5 = 63

1 group + 1 box = 7 p
315 + 63 = 7 p
7 p = 378

1 p = 378 ÷ 7 = 54

3 p = 3 x 54 = 162

1 group + 3 p = 3 u
315 + 162 = 3 u
3 u = 477

1 u = 477 ÷ 3 = 159

Number of erasers that Rachel had at first
= 4 boxes + 1 u
= (4 x 63) + 159
= 252 + 159
= 411

Percent that Rachel had less in the end than at first
= ^{411 - 315}₄₁₁ x 100%
≈ 23.4%

Answer(s): 23.4%