Olivia had 25% more stickers than Ella. Hazel had 50% fewer stickers than Olivia. Olivia and Ella gave Hazel some stickers in the ratio of 3 : 4. As a result, Hazel had 60% more stickers than before. Given that Hazel had 72 more stickers than Ella in the end, how many stickers did Olivia give to Hazel?

Olivia	Ella	Hazel
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Olivia : Ella = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Olivia : Hazel = 2 : 1

The number of stickers that Olivia had at first is repeated. Make the number of stickers that Olivia had at first the same.  LCM of 5 and 2 is 10.

	Olivia	Ella	Hazel
Before	10x7 =  70 u	8x7 = 56 u	5x7 = 35 u
Change			+ 3x7 = + 21 u
Comparing the changes in the number of stickers	- 3x3 = - 9 u	- 4x3 = - 12 u	+ 7x3 = + 21 u
After	61 u	44 u	8x7 = 56 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of stickers that Olivia and Ella gave to Hazel is repeated.  Make the total number of stickers that Olivia and Ella gave to Hazel the same.  LCM of 7 and 3 is 21.

Number of stickers that Hazel had more than Ella 
= 56 u - 44 u
= 12 u

12 u = 72

1 u = 72 ÷ 12 = 6

Number of stickers that Olivia gave to Hazel
= 9 u
= 9 x 6
= 54

Answer(s): 54