Irene has 30% as many cards as Gabby. Gabby has 110% as many cards as Winnie. If Gabby gives 40 cards to Winnie, both will then have an equal number of cards. Find the average number of cards the three of them have.

Irene	Gabby	Winnie
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Gabby	Winnie	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 Gabby and Winnie have
= 110 u + 100 u
= 210 u

After Gabby gives to Winnie, both of them will have the same number of cards. 

The total number of cards that Gabby and Winnie have remains unchanged.

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

Number of cards that Gabby gives to Winnie
= 110 u - 105 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

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 8
= 648

Answer(s): 648