Olivia had 50% more coins than Bryan. Lucy had 20% fewer coins than Olivia. Olivia and Bryan gave Lucy some coins in the ratio of 4 : 5. As a result, Lucy had 50% more coins than before. Given that Bryan had 204 less coins than Lucy in the end, how many coins did Bryan give to Lucy?

Olivia	Bryan	Lucy
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Olivia : Bryan = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Olivia : Lucy = 5 : 4

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

	Olivia	Bryan	Lucy
Before	15x3 =  45 u	10x3 = 30 u	12x3 = 36 u
Change			+ 6x3 = + 18 u
Comparing the changes in the number of coins	- 4x2 = - 8 u	- 5x2 = - 10 u	+ 9x2 = + 18 u
After	37 u	20 u	18x3 = 54 u

50% x 12 
= ⁵⁰₁₀₀ x 12 
= 6 

The total number of coins that Olivia and Bryan gave to Lucy is repeated.  Make the total number of coins that Olivia and Bryan gave to Lucy the same.  LCM of 9 and 6 is 18.

Number of coins that Bryan had less than Lucy 
= 54 u - 20 u
= 34 u

34 u = 204

1 u = 204 ÷ 34 = 6

Number of coins that Bryan gave to Lucy
= 10 u
= 10 x 6
= 60

Answer(s): 60