Emily bought 50% more pens than Joseph. Riordan bought 35% fewer pens than Emily. Emily and Joseph gave Riordan some pens in the ratio 2 : 1. As a result, Riordan had twice as much pens as before. Given that Emily had 18 less pens than Joseph in the end, how much pens did Emily and Joseph give to Riordan?

	Emily	Joseph	Riordan
	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 pens that Emily had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of pens that Riordan had is the repeated identity when Emily and Joseph gave to Riordan.
LCM of 78 and 3 = 78

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

6 u = 18
1 u = 18 ÷ 6 = 3

Number of pens that Emily and Joseph gave to Riordan
= 52 u + 26 u
= 78 u
= 78 x 3
= 234

Answer(s): 234