Emily has 30% as many beads as Anna. Anna has 140% as many beads as Opal. If Anna gives 90 beads to Opal, both will then have an equal number of beads. Find the average number of beads the three of them have.

Emily	Anna	Opal
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

The number of beads that Emily has is repeated.  Make the number of beads that Emily has the same. LCM of 10 and 7 is 70.

	Anna	Opal	Total
Before	70 u	50 u	120 u
Change	- 10 u	+ 10 u
After	60 u	60 u	120 u

Total number of beads that Anna and Opal have
= 70 u + 50 u
= 120 u

After Anna gives to Opal, both of them will have the same number of beads. 

The total number of beads that Anna and Opal have remains unchanged.

Number of beads that each of them will have
= 120 u ÷ 2
= 60 u

Number of beads that Anna gives to Opal
= 70 u - 60 u
= 10 u

10 u = 90

1 u = 90 ÷ 10 = 9

Total number of beads that three of them have
= 120 u + 21 u
= 141 u

Average number of beads that each of them have
= 141 u ÷ 3
= 47 u
= 47 x 9
= 423

Answer(s): 423