Julie had 25% more marbles than Victoria. Josiah had 50% fewer marbles than Julie. Julie and Victoria gave Josiah some marbles in the ratio of 1 : 5. As a result, Josiah had 60% more marbles than before. Given that Victoria had 30 less marbles than Josiah in the end, how many marbles did Victoria give to Josiah?

Julie	Victoria	Josiah
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Julie : Victoria = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Julie : Josiah = 2 : 1

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

	Julie	Victoria	Josiah
Before	10x2 =  20 u	8x2 = 16 u	5x2 = 10 u
Change			+ 3x2 = + 6 u
Comparing the changes in the number of marbles	- 1x1 = - 1 u	- 5x1 = - 5 u	+ 6x1 = + 6 u
After	19 u	11 u	8x2 = 16 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of marbles that Julie and Victoria gave to Josiah is repeated.  Make the total number of marbles that Julie and Victoria gave to Josiah the same.  LCM of 6 and 3 is 6.

Number of marbles that Victoria had less than Josiah 
= 16 u - 11 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

Number of marbles that Victoria gave to Josiah
= 5 u
= 5 x 6
= 30

Answer(s): 30