Emily, Betty and Zoe had 936 cards. Betty won some of the cards from Emily and as a result, Betty's cards increased by 50%. Zoe then won some cards from Betty and Zoe's cards increased by 30%. Finally, Zoe lost some of her cards to Emily and Emily's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Emily have in the end than what she had at first? Correct your answer to 1 decimal place.

Emily	Betty	Zoe
936
	2 u
- 1 u	+ 1 u
	3 u
		10 p
	- 3 p	+ 3 p
		13 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
30% = ³⁰₁₀₀ = ³₁₀
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 936

1 group = 936 ÷ 3 = 312

1 group = 6 boxes
6 boxes = 312

1 box = 312 ÷ 6 = 52

1 group + 1 box = 13 p
312 + 52 = 13 p
13 p = 364

1 p = 364 ÷ 13 = 28

3 p = 3 x 28 = 84

1 group + 3 p = 3 u
312 + 84 = 3 u
3 u = 396

1 u = 396 ÷ 3 = 132

Number of cards that Emily had at first
= 5 boxes + 1 u
= (5 x 52) + 132
= 260 + 132
= 392

Percent that Emily had less in the end than at first
= ^{392 - 312}₃₉₂ x 100%
≈ 20.4%

Answer(s): 20.4%