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

Emily	Irene	Lynn
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Irene	Lynn	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of marbles that Irene and Lynn have
= 110 u + 100 u
= 210 u

After Irene gives to Lynn, both of them will have the same number of marbles. 

The total number of marbles that Irene and Lynn have remains unchanged.

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

Number of marbles that Irene gives to Lynn
= 110 u - 105 u
= 5 u

5 u = 15

1 u = 15 ÷ 5 = 3

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

Average number of marbles that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 3
= 243

Answer(s): 243