Ava had 50% more coins than Raeann. Samantha had 20% fewer coins than Ava. Ava and Raeann gave Samantha some coins in the ratio of 1 : 3. As a result, Samantha had 25% more coins than before. Given that Samantha had 145 more coins than Raeann in the end, how many coins did Ava give to Samantha?

Ava	Raeann	Samantha
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Ava : Raeann = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Ava : Samantha = 5 : 4

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

	Ava	Raeann	Samantha
Before	15x4 =  60 u	10x4 = 40 u	12x4 = 48 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of coins	- 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 coins that Ava and Raeann gave to Samantha is repeated.  Make the total number of coins that Ava and Raeann gave to Samantha the same.  LCM of 4 and 3 is 12.

Number of coins that Samantha had more than Raeann 
= 60 u - 31 u
= 29 u

29 u = 145

1 u = 145 ÷ 29 = 5

Number of coins that Ava gave to Samantha
= 3 u
= 3 x 5
= 15

Answer(s): 15