Sophia bought 50% more buttons than Raeann. David bought 35% fewer buttons than Sophia. Sophia and Raeann gave David some buttons in the ratio 2 : 1. As a result, David had twice as much buttons as before. Given that Sophia had 60 less buttons than Raeann in the end, how much buttons did Sophia and Raeann give to David?

	Sophia	Raeann	David
	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 Sophia had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of buttons that David had is the repeated identity when Sophia and Raeann gave to David.
LCM of 78 and 3 = 78

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

6 u = 60
1 u = 60 ÷ 6 = 10

Number of buttons that Sophia and Raeann gave to David
= 52 u + 26 u
= 78 u
= 78 x 10
= 780

Answer(s): 780