Xylia, Betty and Sarah had 1098 pens. Betty won some of the pens from Xylia and as a result, Betty's pens increased by 50%. Sarah then won some pens from Betty and Sarah's pens increased by 75%. Finally, Sarah lost some of her pens to Xylia and Xylia's pens increased by 20%. In the end, they realised that they each had an equal number of pens. How many percent less did Xylia have in the end than what she had at first? Correct your answer to 1 decimal place.

Xylia	Betty	Sarah
1098
	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 = 1098

1 group = 1098 ÷ 3 = 366

1 group = 6 boxes
6 boxes = 366

1 box = 366 ÷ 6 = 61

1 group + 1 box = 7 p
366 + 61 = 7 p
7 p = 427

1 p = 427 ÷ 7 = 61

3 p = 3 x 61 = 183

1 group + 3 p = 3 u
366 + 183 = 3 u
3 u = 549

1 u = 549 ÷ 3 = 183

Number of pens that Xylia had at first
= 5 boxes + 1 u
= (5 x 61) + 183
= 305 + 183
= 488

Percent that Xylia had less in the end than at first
= ^{488 - 366}₄₈₈ x 100%
≈ 25.0%

Answer(s): 25.0%