Cathy has 30% as many beads as Vanessa. Vanessa has 110% as many beads as Irene. If Vanessa gives 15 beads to Irene, both will then have an equal number of beads. Find the average number of beads the three of them have.

Cathy	Vanessa	Irene
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Vanessa	Irene	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 Vanessa and Irene have
= 110 u + 100 u
= 210 u

After Vanessa gives to Irene, both of them will have the same number of beads. 

The total number of beads that Vanessa and Irene have remains unchanged.

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

Number of beads that Vanessa gives to Irene
= 110 u - 105 u
= 5 u

5 u = 15

1 u = 15 ÷ 5 = 3

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 3
= 243

Answer(s): 243