Jade, Shannon and Gwen had 810 marbles. Shannon won some of the marbles from Jade and as a result, Shannon's marbles increased by 20%. Gwen then won some marbles from Shannon and Gwen's marbles increased by 80%. Finally, Gwen lost some of her marbles to Jade and Jade's marbles increased by 25%. In the end, they realised that they each had an equal number of marbles. How many percent less did Jade have in the end than what she had at first? Correct your answer to 1 decimal place.

Jade	Shannon	Gwen
810
	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 = 810

1 group = 810 ÷ 3 = 270

1 group = 5 boxes
5 boxes = 270

1 box = 270 ÷ 5 = 54

1 group + 1 box = 9 p
270 + 54 = 9 p
9 p = 324

1 p = 324 ÷ 9 = 36

4 p = 4 x 36 = 144

1 group + 4 p = 6 u
270 + 144 = 6 u
6 u = 414

1 u = 414 ÷ 6 = 69

Number of marbles that Jade had at first
= 4 boxes + 1 u
= (4 x 54) + 69
= 216 + 69
= 285

Percent that Jade had less in the end than at first
= ^{285 - 270}₂₈₅ x 100%
≈ 5.3%

Answer(s): 5.3%