Vanessa, Erika and Opal had 810 cards. Erika won some of the cards from Vanessa and as a result, Erika's cards increased by 25%. Opal then won some cards from Erika and Opal's cards increased by 50%. Finally, Opal lost some of her cards to Vanessa and Vanessa's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Vanessa have in the end than what she had at first? Correct your answer to 1 decimal place.

Vanessa	Erika	Opal
810
	4 u
- 1 u	+ 1 u
	5 u
		2 p
	- 1 p	+ 1 p
		3 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

25% = ²⁵₁₀₀ = ¹₄
50% = ⁵⁰₁₀₀ = ¹₂
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 810

1 group = 810 ÷ 3 = 270

1 group = 6 boxes
6 boxes = 270

1 box = 270 ÷ 6 = 45

1 group + 1 box = 3 p
270 + 45 = 3 p
3 p = 315

1 p = 315 ÷ 3 = 105

1 p = 1 x 105 = 105

1 group + 1 p = 5 u
270 + 105 = 5 u
5 u = 375

1 u = 375 ÷ 5 = 75

Number of cards that Vanessa had at first
= 5 boxes + 1 u
= (5 x 45) + 75
= 225 + 75
= 300

Percent that Vanessa had less in the end than at first
= ^{300 - 270}₃₀₀ x 100%
≈ 10.0%

Answer(s): 10.0%