Gabriel had 50% more pencils than Aaron. Emma had 20% fewer pencils than Gabriel. Gabriel and Aaron gave Emma some pencils in the ratio of 1 : 3. As a result, Emma had 25% more pencils than before. Given that Aaron had 261 less pencils than Emma in the end, how many pencils did Aaron give to Emma?

Gabriel	Aaron	Emma
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Gabriel : Aaron = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Gabriel : Emma = 5 : 4

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

	Gabriel	Aaron	Emma
Before	15x4 =  60 u	10x4 = 40 u	12x4 = 48 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of pencils	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	57 u	31 u	15x4 = 60 u

25% x 12 
= ²⁵₁₀₀ x 12 
= 3 

The total number of pencils that Gabriel and Aaron gave to Emma is repeated.  Make the total number of pencils that Gabriel and Aaron gave to Emma the same.  LCM of 4 and 3 is 12.

Number of pencils that Aaron had less than Emma 
= 60 u - 31 u
= 29 u

29 u = 261

1 u = 261 ÷ 29 = 9

Number of pencils that Aaron gave to Emma
= 9 u
= 9 x 9
= 81

Answer(s): 81