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

Harris	Avery	Jeremiah
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Harris : Avery = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Harris : Jeremiah = 5 : 4

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

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

Number of beads that Jeremiah had more than Avery 
= 60 u - 31 u
= 29 u

29 u = 290

1 u = 290 ÷ 29 = 10

Number of beads that Harris gave to Jeremiah
= 3 u
= 3 x 10
= 30

Answer(s): 30