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

	Joseph	Isabella	Audrey
	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 cards that Joseph had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of cards that Audrey had is the repeated identity when Joseph and Isabella gave to Audrey.
LCM of 78 and 3 = 78

Number of cards that Joseph had less than Isabella in the end
= 14 u - 8 u
= 6 u

6 u = 12
1 u = 12 ÷ 6 = 2

Number of cards that Joseph and Isabella gave to Audrey
= 52 u + 26 u
= 78 u
= 78 x 2
= 156

Answer(s): 156