Rachel, Diana and Ivory had 1350 erasers. Diana won some of the erasers from Rachel and as a result, Diana's erasers increased by 50%. Ivory then won some erasers from Diana and Ivory's erasers increased by 75%. Finally, Ivory lost some of her erasers to Rachel and Rachel's erasers increased by 20%. 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	Diana	Ivory
1350
	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 = 1350

1 group = 1350 ÷ 3 = 450

1 group = 6 boxes
6 boxes = 450

1 box = 450 ÷ 6 = 75

1 group + 1 box = 7 p
450 + 75 = 7 p
7 p = 525

1 p = 525 ÷ 7 = 75

3 p = 3 x 75 = 225

1 group + 3 p = 3 u
450 + 225 = 3 u
3 u = 675

1 u = 675 ÷ 3 = 225

Number of erasers that Rachel had at first
= 5 boxes + 1 u
= (5 x 75) + 225
= 375 + 225
= 600

Percent that Rachel had less in the end than at first
= ^{600 - 450}₆₀₀ x 100%
≈ 25.0%

Answer(s): 25.0%