Audrey bought 50% more beads than Jack. Matthew bought 35% fewer beads than Audrey. Audrey and Jack gave Matthew some beads in the ratio 2 : 1. As a result, Matthew had twice as much beads as before. Given that Audrey had 12 less beads than Jack in the end, how much beads did Audrey and Jack give to Matthew?

	Audrey	Jack	Matthew
	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 Audrey had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of beads that Matthew had is the repeated identity when Audrey and Jack gave to Matthew.
LCM of 78 and 3 = 78

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

6 u = 12
1 u = 12 ÷ 6 = 2

Number of beads that Audrey and Jack gave to Matthew
= 52 u + 26 u
= 78 u
= 78 x 2
= 156

Answer(s): 156