Roshel had 50% more marbles than Victoria. Sophia had 20% fewer marbles than Roshel. Roshel and Victoria gave Sophia some marbles in the ratio of 1 : 3. As a result, Sophia had 25% more marbles than before. Given that Victoria had 145 less marbles than Sophia in the end, how many marbles did Victoria give to Sophia?

Roshel	Victoria	Sophia
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Roshel : Victoria = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Roshel : Sophia = 5 : 4

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

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

Number of marbles that Victoria had less than Sophia 
= 60 u - 31 u
= 29 u

29 u = 145

1 u = 145 ÷ 29 = 5

Number of marbles that Victoria gave to Sophia
= 9 u
= 9 x 5
= 45

Answer(s): 45