Wendy, Olivia and Penelope had 1242 buttons. Olivia won some of the buttons from Wendy and as a result, Olivia's buttons increased by 50%. Penelope then won some buttons from Olivia and Penelope's buttons increased by 75%. Finally, Penelope lost some of her buttons to Wendy and Wendy's buttons increased by 20%. In the end, they realised that they each had an equal number of buttons. How many percent less did Wendy have in the end than what she had at first? Correct your answer to 1 decimal place.

Wendy	Olivia	Penelope
1242
	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 = 1242

1 group = 1242 ÷ 3 = 414

1 group = 6 boxes
6 boxes = 414

1 box = 414 ÷ 6 = 69

1 group + 1 box = 7 p
414 + 69 = 7 p
7 p = 483

1 p = 483 ÷ 7 = 69

3 p = 3 x 69 = 207

1 group + 3 p = 3 u
414 + 207 = 3 u
3 u = 621

1 u = 621 ÷ 3 = 207

Number of buttons that Wendy had at first
= 5 boxes + 1 u
= (5 x 69) + 207
= 345 + 207
= 552

Percent that Wendy had less in the end than at first
= ^{552 - 414}₅₅₂ x 100%
≈ 25.0%

Answer(s): 25.0%