Zoe, Xandra and Elyse had 1278 pens. Xandra won some of the pens from Zoe and as a result, Xandra's pens increased by 50%. Elyse then won some pens from Xandra and Elyse's pens increased by 75%. Finally, Elyse lost some of her pens to Zoe and Zoe's pens increased by 20%. In the end, they realised that they each had an equal number of pens. How many percent less did Zoe have in the end than what she had at first? Correct your answer to 1 decimal place.

Zoe	Xandra	Elyse
1278
	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 = 1278

1 group = 1278 ÷ 3 = 426

1 group = 6 boxes
6 boxes = 426

1 box = 426 ÷ 6 = 71

1 group + 1 box = 7 p
426 + 71 = 7 p
7 p = 497

1 p = 497 ÷ 7 = 71

3 p = 3 x 71 = 213

1 group + 3 p = 3 u
426 + 213 = 3 u
3 u = 639

1 u = 639 ÷ 3 = 213

Number of pens that Zoe had at first
= 5 boxes + 1 u
= (5 x 71) + 213
= 355 + 213
= 568

Percent that Zoe had less in the end than at first
= ^{568 - 426}₅₆₈ x 100%
≈ 25.0%

Answer(s): 25.0%