Emily, Zara and Shannon had 1080 pens. Zara won some of the pens from Emily and as a result, Zara's pens increased by 20%. Shannon then won some pens from Zara and Shannon's pens increased by 80%. Finally, Shannon lost some of her pens to Emily and Emily's pens increased by 25%. In the end, they realised that they each had an equal number of pens. How many percent less did Emily have in the end than what she had at first? Correct your answer to 1 decimal place.

Emily	Zara	Shannon
1080
	5 u
- 1 u	+ 1 u
	6 u
		5 p
	- 4 p	+ 4 p
		9 p
4 boxes
+ 1 box		- 1 box
5 boxes
1 group	1 group	1 group

20% = ²⁰₁₀₀ = ¹₅
80% = ⁸⁰₁₀₀ = ⁴₅
25% = ²⁵₁₀₀ = ¹₄

Working backwards.

3 groups = 1080

1 group = 1080 ÷ 3 = 360

1 group = 5 boxes
5 boxes = 360

1 box = 360 ÷ 5 = 72

1 group + 1 box = 9 p
360 + 72 = 9 p
9 p = 432

1 p = 432 ÷ 9 = 48

4 p = 4 x 48 = 192

1 group + 4 p = 6 u
360 + 192 = 6 u
6 u = 552

1 u = 552 ÷ 6 = 92

Number of pens that Emily had at first
= 4 boxes + 1 u
= (4 x 72) + 92
= 288 + 92
= 380

Percent that Emily had less in the end than at first
= ^{380 - 360}₃₈₀ x 100%
≈ 5.3%

Answer(s): 5.3%