John had 40% more stickers than Aria. Olivia had 20% fewer stickers than John. John and Aria gave Olivia some stickers in the ratio of 1 : 3. As a result, Olivia had 50% more stickers than before. Given that Olivia had 495 more stickers than Aria in the end, how many stickers did John give to Olivia?

John	Aria	Olivia
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

John : Aria = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

John : Olivia = 5 : 4

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

	John	Aria	Olivia
Before	35x2 =  70 u	25x2 = 50 u	28x2 = 56 u
Change			+ 14x2 = + 28 u
Comparing the changes in the number of stickers	- 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 stickers that John and Aria gave to Olivia is repeated.  Make the total number of stickers that John and Aria gave to Olivia the same.  LCM of 4 and 14 is 28.

Number of stickers that Olivia had more than Aria 
= 84 u - 29 u
= 55 u

55 u = 495

1 u = 495 ÷ 55 = 9

Number of stickers that John gave to Olivia
= 7 u
= 7 x 9
= 63

Answer(s): 63