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

Yen	Rachel	Dana
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Rachel	Dana	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 Dana have
= 110 u + 100 u
= 210 u

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

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

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

Number of beads that Rachel gives to Dana
= 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