Avery had 50% more erasers than Henry. Nora had 20% fewer erasers than Avery. Avery and Henry gave Nora some erasers in the ratio of 3 : 5. As a result, Nora had 50% more erasers than before. Given that Nora had 423 more erasers than Henry in the end, how many erasers did Avery give to Nora?

Avery	Henry	Nora
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Avery : Henry = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Avery : Nora = 5 : 4

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

	Avery	Henry	Nora
Before	15x4 =  60 u	10x4 = 40 u	12x4 = 48 u
Change			+ 6x4 = + 24 u
Comparing the changes in the number of erasers	- 3x3 = - 9 u	- 5x3 = - 15 u	+ 8x3 = + 24 u
After	51 u	25 u	18x4 = 72 u

50% x 12 
= ⁵⁰₁₀₀ x 12 
= 6 

The total number of erasers that Avery and Henry gave to Nora is repeated.  Make the total number of erasers that Avery and Henry gave to Nora the same.  LCM of 8 and 6 is 24.

Number of erasers that Nora had more than Henry 
= 72 u - 25 u
= 47 u

47 u = 423

1 u = 423 ÷ 47 = 9

Number of erasers that Avery gave to Nora
= 9 u
= 9 x 9
= 81

Answer(s): 81