Dana, Natalie and Cathy had 972 beads. Natalie won some of the beads from Dana and as a result, Natalie's beads increased by 50%. Cathy then won some beads from Natalie and Cathy's beads increased by 40%. Finally, Cathy lost some of her beads to Dana and Dana's beads increased by 20%. In the end, they realised that they each had an equal number of beads. How many percent less did Dana have in the end than what she had at first? Correct your answer to 1 decimal place.

Dana	Natalie	Cathy
972
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 2 p	+ 2 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
40% = ⁴⁰₁₀₀ = ²₅
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 = 7 p
324 + 54 = 7 p
7 p = 378

1 p = 378 ÷ 7 = 54

2 p = 2 x 54 = 108

1 group + 2 p = 3 u
324 + 108 = 3 u
3 u = 432

1 u = 432 ÷ 3 = 144

Number of beads that Dana had at first
= 5 boxes + 1 u
= (5 x 54) + 144
= 270 + 144
= 414

Percent that Dana had less in the end than at first
= ^{414 - 324}₄₁₄ x 100%
≈ 21.7%

Answer(s): 21.7%