Penelope has 30% as many beads as Rachel. Rachel has 110% as many beads as Ivory. If Rachel gives 45 beads to Ivory, both will then have an equal number of beads. Find the average number of beads the three of them have.

Penelope	Rachel	Ivory
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

The number of beads that Penelope has is repeated.  Make the number of beads that Penelope has the same. LCM of 10 and 11 is 110.

	Rachel	Ivory	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of beads that Rachel and Ivory have
= 110 u + 100 u
= 210 u

After Rachel gives to Ivory, both of them will have the same number of beads. 

The total number of beads that Rachel and Ivory have remains unchanged.

Number of beads that each of them will have
= 210 u ÷ 2
= 105 u

Number of beads that Rachel gives to Ivory
= 110 u - 105 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Total number of beads that three of them have
= 210 u + 33 u
= 243 u

Average number of beads that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 9
= 729

Answer(s): 729