Opal, Victoria and Usha had 1170 beads. Victoria won some of the beads from Opal and as a result, Victoria's beads increased by 50%. Usha then won some beads from Victoria and Usha's beads increased by 30%. Finally, Usha lost some of her beads to Opal and Opal's beads increased by 20%. In the end, they realised that they each had an equal number of beads. How many percent less did Opal have in the end than what she had at first? Correct your answer to 1 decimal place.

Opal	Victoria	Usha
1170
	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 = 1170

1 group = 1170 ÷ 3 = 390

1 group = 6 boxes
6 boxes = 390

1 box = 390 ÷ 6 = 65

1 group + 1 box = 13 p
390 + 65 = 13 p
13 p = 455

1 p = 455 ÷ 13 = 35

3 p = 3 x 35 = 105

1 group + 3 p = 3 u
390 + 105 = 3 u
3 u = 495

1 u = 495 ÷ 3 = 165

Number of beads that Opal had at first
= 5 boxes + 1 u
= (5 x 65) + 165
= 325 + 165
= 490

Percent that Opal had less in the end than at first
= ^{490 - 390}₄₉₀ x 100%
≈ 20.4%

Answer(s): 20.4%