Esther, Emily and Xuan had 774 pens. Emily won some of the pens from Esther and as a result, Emily's pens increased by 50%. Xuan then won some pens from Emily and Xuan's pens increased by 75%. Finally, Xuan lost some of her pens to Esther and Esther's pens increased by 20%. In the end, they realised that they each had an equal number of pens. How many percent less did Esther have in the end than what she had at first? Correct your answer to 1 decimal place.

Esther	Emily	Xuan
774
	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 = 774

1 group = 774 ÷ 3 = 258

1 group = 6 boxes
6 boxes = 258

1 box = 258 ÷ 6 = 43

1 group + 1 box = 7 p
258 + 43 = 7 p
7 p = 301

1 p = 301 ÷ 7 = 43

3 p = 3 x 43 = 129

1 group + 3 p = 3 u
258 + 129 = 3 u
3 u = 387

1 u = 387 ÷ 3 = 129

Number of pens that Esther had at first
= 5 boxes + 1 u
= (5 x 43) + 129
= 215 + 129
= 344

Percent that Esther had less in the end than at first
= ^{344 - 258}₃₄₄ x 100%
≈ 25.0%

Answer(s): 25.0%