Zoey had 40% more erasers than Olivia. Ryan had 20% fewer erasers than Zoey. Zoey and Olivia gave Ryan some erasers in the ratio of 1 : 3. As a result, Ryan had 50% more erasers than before. Given that Olivia had 440 less erasers than Ryan in the end, how many erasers did Olivia give to Ryan?

Zoey	Olivia	Ryan
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Zoey : Olivia = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Zoey : Ryan = 5 : 4

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

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

Number of erasers that Olivia had less than Ryan 
= 84 u - 29 u
= 55 u

55 u = 440

1 u = 440 ÷ 55 = 8

Number of erasers that Olivia gave to Ryan
= 21 u
= 21 x 8
= 168

Answer(s): 168