Lucy, Jean and Emily had 1134 marbles. Jean won some of the marbles from Lucy and as a result, Jean's marbles increased by 50%. Emily then won some marbles from Jean and Emily's marbles increased by 75%. Finally, Emily lost some of her marbles to Lucy and Lucy's marbles increased by 20%. In the end, they realised that they each had an equal number of marbles. How many percent less did Lucy have in the end than what she had at first? Correct your answer to 1 decimal place.

Lucy	Jean	Emily
1134
	2 u
- 1 u	+ 1 u
	3 u
		4 p
	- 3 p	+ 3 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
75% = ⁷⁵₁₀₀ = ³₄
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1134

1 group = 1134 ÷ 3 = 378

1 group = 6 boxes
6 boxes = 378

1 box = 378 ÷ 6 = 63

1 group + 1 box = 7 p
378 + 63 = 7 p
7 p = 441

1 p = 441 ÷ 7 = 63

3 p = 3 x 63 = 189

1 group + 3 p = 3 u
378 + 189 = 3 u
3 u = 567

1 u = 567 ÷ 3 = 189

Number of marbles that Lucy had at first
= 5 boxes + 1 u
= (5 x 63) + 189
= 315 + 189
= 504

Percent that Lucy had less in the end than at first
= ^{504 - 378}₅₀₄ x 100%
≈ 25.0%

Answer(s): 25.0%