Xandra has 30% as many coins as Jean. Jean has 110% as many coins as Shiyun. If Jean gives 45 coins to Shiyun, both will then have an equal number of coins. Find the average number of coins the three of them have.

Xandra	Jean	Shiyun
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Jean	Shiyun	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of coins that Jean and Shiyun have
= 110 u + 100 u
= 210 u

After Jean gives to Shiyun, both of them will have the same number of coins. 

The total number of coins that Jean and Shiyun have remains unchanged.

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

Number of coins that Jean gives to Shiyun
= 110 u - 105 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

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

Average number of coins that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 9
= 729

Answer(s): 729