Gillian has 30% as many marbles as Jane. Jane has 110% as many marbles as Emma. If Jane gives 55 marbles to Emma, both will then have an equal number of marbles. Find the average number of marbles the three of them have.

Gillian	Jane	Emma
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Jane	Emma	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 Jane and Emma have
= 110 u + 100 u
= 210 u

After Jane gives to Emma, both of them will have the same number of marbles. 

The total number of marbles that Jane and Emma have remains unchanged.

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

Number of marbles that Jane gives to Emma
= 110 u - 105 u
= 5 u

5 u = 55

1 u = 55 ÷ 5 = 11

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 11
= 891

Answer(s): 891