Betty has 30% as many cards as Jaslyn. Jaslyn has 110% as many cards as Cindy. If Jaslyn gives 45 cards to Cindy, both will then have an equal number of cards. Find the average number of cards the three of them have.

Betty	Jaslyn	Cindy
3x11	10x11
	11x10	10x10
33 u	110 u	100 u

30% = ³⁰₁₀₀ = ³₁₀
110% = ¹¹⁰₁₀₀= ¹¹₁₀

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

	Jaslyn	Cindy	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 Jaslyn and Cindy have
= 110 u + 100 u
= 210 u

After Jaslyn gives to Cindy, both of them will have the same number of cards. 

The total number of cards that Jaslyn and Cindy have remains unchanged.

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

Number of cards that Jaslyn gives to Cindy
= 110 u - 105 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

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 9
= 729

Answer(s): 729