Gwen, Yen and Shannon had 1260 pens. Yen won some of the pens from Gwen and as a result, Yen's pens increased by 50%. Shannon then won some pens from Yen and Shannon's pens increased by 60%. Finally, Shannon lost some of her pens to Gwen and Gwen's pens increased by 25%. In the end, they realised that they each had an equal number of pens. How many percent less did Gwen have in the end than what she had at first? Correct your answer to 1 decimal place.

Gwen	Yen	Shannon
1260
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 3 p	+ 3 p
		8 p
4 boxes
+ 1 box		- 1 box
5 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
60% = ⁶⁰₁₀₀ = ³₅
25% = ²⁵₁₀₀ = ¹₄

Working backwards.

3 groups = 1260

1 group = 1260 ÷ 3 = 420

1 group = 5 boxes
5 boxes = 420

1 box = 420 ÷ 5 = 84

1 group + 1 box = 8 p
420 + 84 = 8 p
8 p = 504

1 p = 504 ÷ 8 = 63

3 p = 3 x 63 = 189

1 group + 3 p = 3 u
420 + 189 = 3 u
3 u = 609

1 u = 609 ÷ 3 = 203

Number of pens that Gwen had at first
= 4 boxes + 1 u
= (4 x 84) + 203
= 336 + 203
= 539

Percent that Gwen had less in the end than at first
= ^{539 - 420}₅₃₉ x 100%
≈ 22.1%

Answer(s): 22.1%