Kathy, Esther and Cathy had 720 cards. Esther won some of the cards from Kathy and as a result, Esther's cards increased by 50%. Cathy then won some cards from Esther and Cathy's cards increased by 75%. Finally, Cathy lost some of her cards to Kathy and Kathy's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Kathy have in the end than what she had at first? Correct your answer to 1 decimal place.

Kathy	Esther	Cathy
720
	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 = 720

1 group = 720 ÷ 3 = 240

1 group = 6 boxes
6 boxes = 240

1 box = 240 ÷ 6 = 40

1 group + 1 box = 7 p
240 + 40 = 7 p
7 p = 280

1 p = 280 ÷ 7 = 40

3 p = 3 x 40 = 120

1 group + 3 p = 3 u
240 + 120 = 3 u
3 u = 360

1 u = 360 ÷ 3 = 120

Number of cards that Kathy had at first
= 5 boxes + 1 u
= (5 x 40) + 120
= 200 + 120
= 320

Percent that Kathy had less in the end than at first
= ^{320 - 240}₃₂₀ x 100%
≈ 25.0%

Answer(s): 25.0%