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

Olivia	Opal	Barbara
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 buttons that Olivia had at first
= 5 boxes + 1 u
= (5 x 40) + 120
= 200 + 120
= 320

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

Answer(s): 25.0%