Maya had 50% more erasers than Emily. William had 20% fewer erasers than Maya. Maya and Emily gave William some erasers in the ratio of 1 : 3. As a result, William had 50% more erasers than before. Given that William had 300 more erasers than Emily in the end, how many erasers did Maya give to William?

Maya	Emily	William
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Maya : Emily = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Maya : William = 5 : 4

The number of erasers that Maya had at first is repeated. Make the number of erasers that Maya had at first the same.  LCM of 3 and 5 is 15.

	Maya	Emily	William
Before	15x2 =  30 u	10x2 = 20 u	12x2 = 24 u
Change			+ 6x2 = + 12 u
Comparing the changes in the number of erasers	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	27 u	11 u	18x2 = 36 u

50% x 12 
= ⁵⁰₁₀₀ x 12 
= 6 

The total number of erasers that Maya and Emily gave to William is repeated.  Make the total number of erasers that Maya and Emily gave to William the same.  LCM of 4 and 6 is 12.

Number of erasers that William had more than Emily 
= 36 u - 11 u
= 25 u

25 u = 300

1 u = 300 ÷ 25 = 12

Number of erasers that Maya gave to William
= 3 u
= 3 x 12
= 36

Answer(s): 36