Harper had 50% more erasers than John. Oliver had 20% fewer erasers than Harper. Harper and John gave Oliver some erasers in the ratio of 3 : 5. As a result, Oliver had 50% more erasers than before. Given that Oliver had 329 more erasers than John in the end, how many erasers did Harper give to Oliver?

Harper	John	Oliver
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Harper : John = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Harper : Oliver = 5 : 4

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

	Harper	John	Oliver
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 Harper and John gave to Oliver is repeated.  Make the total number of erasers that Harper and John gave to Oliver the same.  LCM of 8 and 6 is 24.

Number of erasers that Oliver had more than John 
= 72 u - 25 u
= 47 u

47 u = 329

1 u = 329 ÷ 47 = 7

Number of erasers that Harper gave to Oliver
= 9 u
= 9 x 7
= 63

Answer(s): 63