Hazel had 50% more marbles than Sebastian. Stella had 20% fewer marbles than Hazel. Hazel and Sebastian gave Stella some marbles in the ratio of 1 : 5. As a result, Stella had 25% more marbles than before. Given that Sebastian had 90 less marbles than Stella in the end, how many marbles did Sebastian give to Stella?

Hazel	Sebastian	Stella
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Hazel : Sebastian = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Hazel : Stella = 5 : 4

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

	Hazel	Sebastian	Stella
Before	15x2 =  30 u	10x2 = 20 u	12x2 = 24 u
Change			+ 3x2 = + 6 u
Comparing the changes in the number of marbles	- 1x1 = - 1 u	- 5x1 = - 5 u	+ 6x1 = + 6 u
After	29 u	15 u	15x2 = 30 u

25% x 12 
= ²⁵₁₀₀ x 12 
= 3 

The total number of marbles that Hazel and Sebastian gave to Stella is repeated.  Make the total number of marbles that Hazel and Sebastian gave to Stella the same.  LCM of 6 and 3 is 6.

Number of marbles that Sebastian had less than Stella 
= 30 u - 15 u
= 15 u

15 u = 90

1 u = 90 ÷ 15 = 6

Number of marbles that Sebastian gave to Stella
= 5 u
= 5 x 6
= 30

Answer(s): 30