Sofia had 40% more stickers than Mia. Henry had 20% fewer stickers than Sofia. Sofia and Mia gave Henry some stickers in the ratio of 1 : 3. As a result, Henry had 50% more stickers than before. Given that Henry had 440 more stickers than Mia in the end, how many stickers did Sofia give to Henry?

Sofia	Mia	Henry
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Sofia : Mia = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Sofia : Henry = 5 : 4

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

	Sofia	Mia	Henry
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 Sofia and Mia gave to Henry is repeated.  Make the total number of stickers that Sofia and Mia gave to Henry the same.  LCM of 4 and 14 is 28.

Number of stickers that Henry had more than Mia 
= 84 u - 29 u
= 55 u

55 u = 440

1 u = 440 ÷ 55 = 8

Number of stickers that Sofia gave to Henry
= 7 u
= 7 x 8
= 56

Answer(s): 56