Nathan had 25% more beads than Jackson. Oliver had 50% fewer beads than Nathan. Nathan and Jackson gave Oliver some beads in the ratio of 1 : 3. As a result, Oliver had 60% more beads than before. Given that Jackson had 45 less beads than Oliver in the end, how many beads did Jackson give to Oliver?

Nathan	Jackson	Oliver
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Nathan : Jackson = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Nathan : Oliver = 2 : 1

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

	Nathan	Jackson	Oliver
Before	10x4 =  40 u	8x4 = 32 u	5x4 = 20 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of beads	- 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 beads that Nathan and Jackson gave to Oliver is repeated.  Make the total number of beads that Nathan and Jackson gave to Oliver the same.  LCM of 4 and 3 is 12.

Number of beads that Jackson had less than Oliver 
= 32 u - 23 u
= 9 u

9 u = 45

1 u = 45 ÷ 9 = 5

Number of beads that Jackson gave to Oliver
= 9 u
= 9 x 5
= 45

Answer(s): 45