Roshel, Nicole and Mary had 675 beads. Nicole won some of the beads from Roshel and as a result, Nicole's beads increased by 50%. Mary then won some beads from Nicole and Mary's beads increased by 80%. Finally, Mary lost some of her beads to Roshel and Roshel's beads increased by 25%. In the end, they realised that they each had an equal number of beads. How many percent less did Roshel have in the end than what she had at first? Correct your answer to 1 decimal place.

Roshel	Nicole	Mary
675
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 4 p	+ 4 p
		9 p
4 boxes
+ 1 box		- 1 box
5 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
80% = ⁸⁰₁₀₀ = ⁴₅
25% = ²⁵₁₀₀ = ¹₄

Working backwards.

3 groups = 675

1 group = 675 ÷ 3 = 225

1 group = 5 boxes
5 boxes = 225

1 box = 225 ÷ 5 = 45

1 group + 1 box = 9 p
225 + 45 = 9 p
9 p = 270

1 p = 270 ÷ 9 = 30

4 p = 4 x 30 = 120

1 group + 4 p = 3 u
225 + 120 = 3 u
3 u = 345

1 u = 345 ÷ 3 = 115

Number of beads that Roshel had at first
= 4 boxes + 1 u
= (4 x 45) + 115
= 180 + 115
= 295

Percent that Roshel had less in the end than at first
= ^{295 - 225}₂₉₅ x 100%
≈ 23.7%

Answer(s): 23.7%