Zoey had 40% more marbles than Henry. Rebecca had 20% fewer marbles than Zoey. Zoey and Henry gave Rebecca some marbles in the ratio of 1 : 3. As a result, Rebecca had 50% more marbles than before. Given that Rebecca had 605 more marbles than Henry in the end, how many marbles did Zoey give to Rebecca?

Zoey	Henry	Rebecca
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Zoey : Henry = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Zoey : Rebecca = 5 : 4

The number of marbles that Zoey had at first is repeated. Make the number of marbles that Zoey had at first the same.  LCM of 7 and 5 is 35.

	Zoey	Henry	Rebecca
Before	35x2 =  70 u	25x2 = 50 u	28x2 = 56 u
Change			+ 14x2 = + 28 u
Comparing the changes in the number of marbles	- 1x7 = - 7 u	- 3x7 = - 21 u	+ 4x7 = + 28 u
After	63 u	29 u	42x2 = 84 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of marbles that Zoey and Henry gave to Rebecca is repeated.  Make the total number of marbles that Zoey and Henry gave to Rebecca the same.  LCM of 4 and 14 is 28.

Number of marbles that Rebecca had more than Henry 
= 84 u - 29 u
= 55 u

55 u = 605

1 u = 605 ÷ 55 = 11

Number of marbles that Zoey gave to Rebecca
= 7 u
= 7 x 11
= 77

Answer(s): 77