Gwen has 30% as many marbles as Winnie. Winnie has 110% as many marbles as Esther. If Winnie gives 40 marbles to Esther, both will then have an equal number of marbles. Find the average number of marbles the three of them have.

Gwen	Winnie	Esther
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Winnie	Esther	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 Winnie and Esther have
= 110 u + 100 u
= 210 u

After Winnie gives to Esther, both of them will have the same number of marbles. 

The total number of marbles that Winnie and Esther have remains unchanged.

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

Number of marbles that Winnie gives to Esther
= 110 u - 105 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

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 8
= 648

Answer(s): 648