Jonathan bought 50% more buttons than Stella. William bought 35% fewer buttons than Jonathan. Jonathan and Stella gave William some buttons in the ratio 2 : 1. As a result, William had twice as much buttons as before. Given that Jonathan had 36 less buttons than Stella in the end, how much buttons did Jonathan and Stella give to William?

	Jonathan	Stella	William
	3x20	2x20
	20x3		13x3
Before	60 u	40 u	39 u
Change			+ (2 x 39 u) = + 78 u
	- 2x26 = - 52 u	- 1x26 = - 26 u	+ 3x26 =  + 78 u
After	8 u	14 u	117 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

The number of buttons that Jonathan had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of buttons that William had is the repeated identity when Jonathan and Stella gave to William.
LCM of 78 and 3 = 78

Number of buttons that Jonathan had less than Stella in the end
= 14 u - 8 u
= 6 u

6 u = 36
1 u = 36 ÷ 6 = 6

Number of buttons that Jonathan and Stella gave to William
= 52 u + 26 u
= 78 u
= 78 x 6
= 468

Answer(s): 468