Aria had 50% more coins than Samantha. Sofia had 20% fewer coins than Aria. Aria and Samantha gave Sofia some coins in the ratio of 4 : 5. As a result, Sofia had 25% more coins than before. Given that Samantha had 100 less coins than Sofia in the end, how many coins did Samantha give to Sofia?

Aria	Samantha	Sofia
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Aria : Samantha = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Aria : Sofia = 5 : 4

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

	Aria	Samantha	Sofia
Before	15x3 =  45 u	10x3 = 30 u	12x3 = 36 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of coins	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	41 u	25 u	15x3 = 45 u

25% x 12 
= ²⁵₁₀₀ x 12 
= 3 

The total number of coins that Aria and Samantha gave to Sofia is repeated.  Make the total number of coins that Aria and Samantha gave to Sofia the same.  LCM of 9 and 3 is 9.

Number of coins that Samantha had less than Sofia 
= 45 u - 25 u
= 20 u

20 u = 100

1 u = 100 ÷ 20 = 5

Number of coins that Samantha gave to Sofia
= 5 u
= 5 x 5
= 25

Answer(s): 25