Rachel has 30% as many coins as Xuan. Xuan has 110% as many coins as Emma. If Xuan gives 20 coins to Emma, both will then have an equal number of coins. Find the average number of coins the three of them have.

Rachel	Xuan	Emma
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

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

After Xuan gives to Emma, both of them will have the same number of coins. 

The total number of coins that Xuan and Emma have remains unchanged.

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

Number of coins that Xuan gives to Emma
= 110 u - 105 u
= 5 u

5 u = 20

1 u = 20 ÷ 5 = 4

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 4
= 324

Answer(s): 324