Gwen has 30% as many beads as Kylie. Kylie has 110% as many beads as Gem. If Kylie gives 10 beads to Gem, both will then have an equal number of beads. Find the average number of beads the three of them have.

Gwen	Kylie	Gem
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Kylie	Gem	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 Kylie and Gem have
= 110 u + 100 u
= 210 u

After Kylie gives to Gem, both of them will have the same number of beads. 

The total number of beads that Kylie and Gem have remains unchanged.

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

Number of beads that Kylie gives to Gem
= 110 u - 105 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

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 2
= 162

Answer(s): 162