Evan had 50% more pens than Christopher. Rael had 20% fewer pens than Evan. Evan and Christopher gave Rael some pens in the ratio of 1 : 3. As a result, Rael had 50% more pens than before. Given that Rael had 125 more pens than Christopher in the end, how many pens did Evan give to Rael?

Evan	Christopher	Rael
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Evan : Christopher = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Evan : Rael = 5 : 4

The number of pens that Evan had at first is repeated. Make the number of pens that Evan had at first the same.  LCM of 3 and 5 is 15.

	Evan	Christopher	Rael
Before	15x2 =  30 u	10x2 = 20 u	12x2 = 24 u
Change			+ 6x2 = + 12 u
Comparing the changes in the number of pens	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	27 u	11 u	18x2 = 36 u

50% x 12 
= ⁵⁰₁₀₀ x 12 
= 6 

The total number of pens that Evan and Christopher gave to Rael is repeated.  Make the total number of pens that Evan and Christopher gave to Rael the same.  LCM of 4 and 6 is 12.

Number of pens that Rael had more than Christopher 
= 36 u - 11 u
= 25 u

25 u = 125

1 u = 125 ÷ 25 = 5

Number of pens that Evan gave to Rael
= 3 u
= 3 x 5
= 15

Answer(s): 15