Olivia has 30% as many cards as Barbara. Barbara has 140% as many cards as Tina. If Barbara gives 110 cards to Tina, both will then have an equal number of cards. Find the average number of cards the three of them have.

Olivia	Barbara	Tina
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

The number of cards that Olivia has is repeated.  Make the number of cards that Olivia has the same. LCM of 10 and 7 is 70.

	Barbara	Tina	Total
Before	70 u	50 u	120 u
Change	- 10 u	+ 10 u
After	60 u	60 u	120 u

Total number of cards that Barbara and Tina have
= 70 u + 50 u
= 120 u

After Barbara gives to Tina, both of them will have the same number of cards. 

The total number of cards that Barbara and Tina have remains unchanged.

Number of cards that each of them will have
= 120 u ÷ 2
= 60 u

Number of cards that Barbara gives to Tina
= 70 u - 60 u
= 10 u

10 u = 110

1 u = 110 ÷ 10 = 11

Total number of cards that three of them have
= 120 u + 21 u
= 141 u

Average number of cards that each of them have
= 141 u ÷ 3
= 47 u
= 47 x 11
= 517

Answer(s): 517