Sarah, Olivia and Pamela had 1296 beads. Olivia won some of the beads from Sarah and as a result, Olivia's beads increased by 50%. Pamela then won some beads from Olivia and Pamela's beads increased by 60%. Finally, Pamela lost some of her beads to Sarah and Sarah's beads increased by 20%. In the end, they realised that they each had an equal number of beads. How many percent less did Sarah have in the end than what she had at first? Correct your answer to 1 decimal place.

Sarah	Olivia	Pamela
1296
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 3 p	+ 3 p
		8 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
60% = ⁶⁰₁₀₀ = ³₅
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1296

1 group = 1296 ÷ 3 = 432

1 group = 6 boxes
6 boxes = 432

1 box = 432 ÷ 6 = 72

1 group + 1 box = 8 p
432 + 72 = 8 p
8 p = 504

1 p = 504 ÷ 8 = 63

3 p = 3 x 63 = 189

1 group + 3 p = 3 u
432 + 189 = 3 u
3 u = 621

1 u = 621 ÷ 3 = 207

Number of beads that Sarah had at first
= 5 boxes + 1 u
= (5 x 72) + 207
= 360 + 207
= 567

Percent that Sarah had less in the end than at first
= ^{567 - 432}₅₆₇ x 100%
≈ 23.8%

Answer(s): 23.8%