Layla had 40% more marbles than Bryan. Noah had 20% fewer marbles than Layla. Layla and Bryan gave Noah some marbles in the ratio of 1 : 3. As a result, Noah had 50% more marbles than before. Given that Noah had 550 more marbles than Bryan in the end, how many marbles did Layla give to Noah?

Layla	Bryan	Noah
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Layla : Bryan = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Layla : Noah = 5 : 4

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

	Layla	Bryan	Noah
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 Layla and Bryan gave to Noah is repeated.  Make the total number of marbles that Layla and Bryan gave to Noah the same.  LCM of 4 and 14 is 28.

Number of marbles that Noah had more than Bryan 
= 84 u - 29 u
= 55 u

55 u = 550

1 u = 550 ÷ 55 = 10

Number of marbles that Layla gave to Noah
= 7 u
= 7 x 10
= 70

Answer(s): 70