Owen had 25% more coins than Isabella. Chloe had 50% fewer coins than Owen. Owen and Isabella gave Chloe some coins in the ratio of 1 : 3. As a result, Chloe had 60% more coins than before. Given that Isabella had 54 less coins than Chloe in the end, how many coins did Isabella give to Chloe?

Owen	Isabella	Chloe
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Owen : Isabella = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Owen : Chloe = 2 : 1

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

	Owen	Isabella	Chloe
Before	10x4 =  40 u	8x4 = 32 u	5x4 = 20 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of coins	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	37 u	23 u	8x4 = 32 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of coins that Owen and Isabella gave to Chloe is repeated.  Make the total number of coins that Owen and Isabella gave to Chloe the same.  LCM of 4 and 3 is 12.

Number of coins that Isabella had less than Chloe 
= 32 u - 23 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Number of coins that Isabella gave to Chloe
= 9 u
= 9 x 6
= 54

Answer(s): 54