Elyse, Jen and Opal had 1404 marbles. Jen won some of the marbles from Elyse and as a result, Jen's marbles increased by 50%. Opal then won some marbles from Jen and Opal's marbles increased by 30%. Finally, Opal lost some of her marbles to Elyse and Elyse's marbles increased by 20%. In the end, they realised that they each had an equal number of marbles. How many percent less did Elyse have in the end than what she had at first? Correct your answer to 1 decimal place.

Elyse	Jen	Opal
1404
	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 = 1404

1 group = 1404 ÷ 3 = 468

1 group = 6 boxes
6 boxes = 468

1 box = 468 ÷ 6 = 78

1 group + 1 box = 13 p
468 + 78 = 13 p
13 p = 546

1 p = 546 ÷ 13 = 42

3 p = 3 x 42 = 126

1 group + 3 p = 3 u
468 + 126 = 3 u
3 u = 594

1 u = 594 ÷ 3 = 198

Number of marbles that Elyse had at first
= 5 boxes + 1 u
= (5 x 78) + 198
= 390 + 198
= 588

Percent that Elyse had less in the end than at first
= ^{588 - 468}₅₈₈ x 100%
≈ 20.4%

Answer(s): 20.4%