Chloe had 40% more erasers than William. Dylan had 20% fewer erasers than Chloe. Chloe and William gave Dylan some erasers in the ratio of 3 : 4. As a result, Dylan had 50% more erasers than before. Given that William had 50 less erasers than Dylan in the end, how many erasers did William give to Dylan?

Chloe	William	Dylan
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Chloe : William = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Chloe : Dylan = 5 : 4

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

	Chloe	William	Dylan
Before	35x1 =  35 u	25x1 = 25 u	28x1 = 28 u
Change			+ 14x1 = + 14 u
Comparing the changes in the number of erasers	- 3x2 = - 6 u	- 4x2 = - 8 u	+ 7x2 = + 14 u
After	29 u	17 u	42x1 = 42 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of erasers that Chloe and William gave to Dylan is repeated.  Make the total number of erasers that Chloe and William gave to Dylan the same.  LCM of 7 and 14 is 14.

Number of erasers that William had less than Dylan 
= 42 u - 17 u
= 25 u

25 u = 50

1 u = 50 ÷ 25 = 2

Number of erasers that William gave to Dylan
= 8 u
= 8 x 2
= 16

Answer(s): 16