Amelia had 25% more pencils than Rebecca. Caleb had 50% fewer pencils than Amelia. Amelia and Rebecca gave Caleb some pencils in the ratio of 4 : 5. As a result, Caleb had 60% more pencils than before. Given that Rebecca had 55 less pencils than Caleb in the end, how many pencils did Rebecca give to Caleb?

Amelia	Rebecca	Caleb
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Amelia : Rebecca = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Amelia : Caleb = 2 : 1

The number of pencils that Amelia had at first is repeated. Make the number of pencils that Amelia had at first the same.  LCM of 5 and 2 is 10.

	Amelia	Rebecca	Caleb
Before	10x3 =  30 u	8x3 = 24 u	5x3 = 15 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of pencils	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	26 u	19 u	8x3 = 24 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of pencils that Amelia and Rebecca gave to Caleb is repeated.  Make the total number of pencils that Amelia and Rebecca gave to Caleb the same.  LCM of 9 and 3 is 9.

Number of pencils that Rebecca had less than Caleb 
= 24 u - 19 u
= 5 u

5 u = 55

1 u = 55 ÷ 5 = 11

Number of pencils that Rebecca gave to Caleb
= 5 u
= 5 x 11
= 55

Answer(s): 55