Diana, Cindy and Emily had 702 coins. Cindy won some of the coins from Diana and as a result, Cindy's coins increased by 50%. Emily then won some coins from Cindy and Emily's coins increased by 40%. Finally, Emily lost some of her coins to Diana and Diana's coins increased by 20%. In the end, they realised that they each had an equal number of coins. How many percent less did Diana have in the end than what she had at first? Correct your answer to 1 decimal place.

Diana	Cindy	Emily
702
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 2 p	+ 2 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
40% = ⁴⁰₁₀₀ = ²₅
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 702

1 group = 702 ÷ 3 = 234

1 group = 6 boxes
6 boxes = 234

1 box = 234 ÷ 6 = 39

1 group + 1 box = 7 p
234 + 39 = 7 p
7 p = 273

1 p = 273 ÷ 7 = 39

2 p = 2 x 39 = 78

1 group + 2 p = 3 u
234 + 78 = 3 u
3 u = 312

1 u = 312 ÷ 3 = 104

Number of coins that Diana had at first
= 5 boxes + 1 u
= (5 x 39) + 104
= 195 + 104
= 299

Percent that Diana had less in the end than at first
= ^{299 - 234}₂₉₉ x 100%
≈ 21.7%

Answer(s): 21.7%