Abi has 30% as many cards as Ivory. Ivory has 140% as many cards as Cathy. If Ivory gives 100 cards to Cathy, both will then have an equal number of cards. Find the average number of cards the three of them have.

Abi	Ivory	Cathy
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

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

	Ivory	Cathy	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 Ivory and Cathy have
= 70 u + 50 u
= 120 u

After Ivory gives to Cathy, both of them will have the same number of cards. 

The total number of cards that Ivory and Cathy have remains unchanged.

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

Number of cards that Ivory gives to Cathy
= 70 u - 60 u
= 10 u

10 u = 100

1 u = 100 ÷ 10 = 10

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 10
= 470

Answer(s): 470