Shannon, Min and Penelope had 684 beads. Min won some of the beads from Shannon and as a result, Min's beads increased by 50%. Penelope then won some beads from Min and Penelope's beads increased by 75%. Finally, Penelope lost some of her beads to Shannon and Shannon's beads increased by 20%. In the end, they realised that they each had an equal number of beads. How many percent less did Shannon have in the end than what she had at first? Correct your answer to 1 decimal place.

Shannon	Min	Penelope
684
	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 = 684

1 group = 684 ÷ 3 = 228

1 group = 6 boxes
6 boxes = 228

1 box = 228 ÷ 6 = 38

1 group + 1 box = 7 p
228 + 38 = 7 p
7 p = 266

1 p = 266 ÷ 7 = 38

3 p = 3 x 38 = 114

1 group + 3 p = 3 u
228 + 114 = 3 u
3 u = 342

1 u = 342 ÷ 3 = 114

Number of beads that Shannon had at first
= 5 boxes + 1 u
= (5 x 38) + 114
= 190 + 114
= 304

Percent that Shannon had less in the end than at first
= ^{304 - 228}₃₀₄ x 100%
≈ 25.0%

Answer(s): 25.0%