Opal, Pamela and Sarah had 972 marbles. Pamela won some of the marbles from Opal and as a result, Pamela's marbles increased by 25%. Sarah then won some marbles from Pamela and Sarah's marbles increased by 50%. Finally, Sarah lost some of her marbles to Opal and Opal's marbles increased by 20%. In the end, they realised that they each had an equal number of marbles. How many percent less did Opal have in the end than what she had at first? Correct your answer to 1 decimal place.

Opal	Pamela	Sarah
972
	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 = 972

1 group = 972 ÷ 3 = 324

1 group = 6 boxes
6 boxes = 324

1 box = 324 ÷ 6 = 54

1 group + 1 box = 3 p
324 + 54 = 3 p
3 p = 378

1 p = 378 ÷ 3 = 126

1 p = 1 x 126 = 126

1 group + 1 p = 5 u
324 + 126 = 5 u
5 u = 450

1 u = 450 ÷ 5 = 90

Number of marbles that Opal had at first
= 5 boxes + 1 u
= (5 x 54) + 90
= 270 + 90
= 360

Percent that Opal had less in the end than at first
= ^{360 - 324}₃₆₀ x 100%
≈ 10.0%

Answer(s): 10.0%