Hilda has 30% as many cards as Usha. Usha has 110% as many cards as Xandra. If Usha gives 30 cards to Xandra, both will then have an equal number of cards. Find the average number of cards the three of them have.

Hilda	Usha	Xandra
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Usha	Xandra	Total
Before	110 u	100 u	210 u
Change	- 5 u	+ 5 u
After	105 u	105 u	210 u

Total number of cards that Usha and Xandra have
= 110 u + 100 u
= 210 u

After Usha gives to Xandra, both of them will have the same number of cards. 

The total number of cards that Usha and Xandra have remains unchanged.

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

Number of cards that Usha gives to Xandra
= 110 u - 105 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

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

Average number of cards that each of them have
= 243 u ÷ 3
= 81 u
= 81 x 6
= 486

Answer(s): 486