Rachel has 30% as many coins as Esther. Esther has 110% as many coins as Kimberly. If Esther gives 10 coins to Kimberly, both will then have an equal number of coins. Find the average number of coins the three of them have.

Rachel	Esther	Kimberly
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.

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

After Esther gives to Kimberly, both of them will have the same number of coins. 

The total number of coins that Esther and Kimberly have remains unchanged.

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

Number of coins that Esther gives to Kimberly
= 110 u - 105 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

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 2
= 162

Answer(s): 162