Emma has 30% as many marbles as Penelope. Penelope has 140% as many marbles as Cindy. If Penelope gives 90 marbles to Cindy, both will then have an equal number of marbles. Find the average number of marbles the three of them have.

Emma	Penelope	Cindy
3x7	10x7
	7x10	5x10
21 u	70 u	50 u

30% = ³⁰₁₀₀ = ³₁₀
140% = ¹⁴⁰₁₀₀= ⁷₅

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

	Penelope	Cindy	Total
Before	70 u	50 u	120 u
Change	- 10 u	+ 10 u
After	60 u	60 u	120 u

Total number of marbles that Penelope and Cindy have
= 70 u + 50 u
= 120 u

After Penelope gives to Cindy, both of them will have the same number of marbles. 

The total number of marbles that Penelope and Cindy have remains unchanged.

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

Number of marbles that Penelope gives to Cindy
= 70 u - 60 u
= 10 u

10 u = 90

1 u = 90 ÷ 10 = 9

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

Average number of marbles that each of them have
= 141 u ÷ 3
= 47 u
= 47 x 9
= 423

Answer(s): 423