Gem, Jane and Ivory had 792 cards. Jane won some of the cards from Gem and as a result, Jane's cards increased by 50%. Ivory then won some cards from Jane and Ivory's cards increased by 75%. Finally, Ivory lost some of her cards to Gem and Gem's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Gem have in the end than what she had at first? Correct your answer to 1 decimal place.

Gem	Jane	Ivory
792
	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 = 792

1 group = 792 ÷ 3 = 264

1 group = 6 boxes
6 boxes = 264

1 box = 264 ÷ 6 = 44

1 group + 1 box = 7 p
264 + 44 = 7 p
7 p = 308

1 p = 308 ÷ 7 = 44

3 p = 3 x 44 = 132

1 group + 3 p = 3 u
264 + 132 = 3 u
3 u = 396

1 u = 396 ÷ 3 = 132

Number of cards that Gem had at first
= 5 boxes + 1 u
= (5 x 44) + 132
= 220 + 132
= 352

Percent that Gem had less in the end than at first
= ^{352 - 264}₃₅₂ x 100%
≈ 25.0%

Answer(s): 25.0%