Scarlett bought 50% more beads than Jeremiah. Olivia bought 35% fewer beads than Scarlett. Scarlett and Jeremiah gave Olivia some beads in the ratio 2 : 1. As a result, Olivia had twice as much beads as before. Given that Scarlett had 54 less beads than Jeremiah in the end, how much beads did Scarlett and Jeremiah give to Olivia?

	Scarlett	Jeremiah	Olivia
	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 beads that Scarlett had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of beads that Olivia had is the repeated identity when Scarlett and Jeremiah gave to Olivia.
LCM of 78 and 3 = 78

Number of beads that Scarlett had less than Jeremiah in the end
= 14 u - 8 u
= 6 u

6 u = 54
1 u = 54 ÷ 6 = 9

Number of beads that Scarlett and Jeremiah gave to Olivia
= 52 u + 26 u
= 78 u
= 78 x 9
= 702

Answer(s): 702