Salik had 50% more buttons than Aubrey. Isabella had 20% fewer buttons than Salik. Salik and Aubrey gave Isabella some buttons in the ratio of 1 : 3. As a result, Isabella had 25% more buttons than before. Given that Isabella had 290 more buttons than Aubrey in the end, how many buttons did Salik give to Isabella?

Salik	Aubrey	Isabella
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Salik : Aubrey = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Salik : Isabella = 5 : 4

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

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

Number of buttons that Isabella had more than Aubrey 
= 60 u - 31 u
= 29 u

29 u = 290

1 u = 290 ÷ 29 = 10

Number of buttons that Salik gave to Isabella
= 3 u
= 3 x 10
= 30

Answer(s): 30