Christopher had 25% more buttons than Dylan. Ethan had 50% fewer buttons than Christopher. Christopher and Dylan gave Ethan some buttons in the ratio of 1 : 5. As a result, Ethan had 60% more buttons than before. Given that Dylan had 35 less buttons than Ethan in the end, how many buttons did Dylan give to Ethan?

Christopher	Dylan	Ethan
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Christopher : Dylan = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Christopher : Ethan = 2 : 1

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

	Christopher	Dylan	Ethan
Before	10x2 =  20 u	8x2 = 16 u	5x2 = 10 u
Change			+ 3x2 = + 6 u
Comparing the changes in the number of buttons	- 1x1 = - 1 u	- 5x1 = - 5 u	+ 6x1 = + 6 u
After	19 u	11 u	8x2 = 16 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of buttons that Christopher and Dylan gave to Ethan is repeated.  Make the total number of buttons that Christopher and Dylan gave to Ethan the same.  LCM of 6 and 3 is 6.

Number of buttons that Dylan had less than Ethan 
= 16 u - 11 u
= 5 u

5 u = 35

1 u = 35 ÷ 5 = 7

Number of buttons that Dylan gave to Ethan
= 5 u
= 5 x 7
= 35

Answer(s): 35