Isaiah had 20% more erasers than Lucy. Harris had 40% fewer erasers than Isaiah. Isaiah and Lucy gave Harris some erasers in the ratio of 1 : 5. As a result, Harris had 50% more erasers than before. Given that Lucy had 171 less erasers than Harris in the end, how many erasers did Lucy give to Harris?

Isaiah	Lucy	Harris
6x5	5x5
5x6		3x6
30	25	18

100% + 20% = 120%
120% = ¹²⁰₁₀₀ = ⁶₅

Isaiah : Lucy = 6 : 5

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

Isaiah : Harris = 5 : 3

The number of erasers that Isaiah had at first is repeated. Make the number of erasers that Isaiah had at first the same.  LCM of 6 and 5 is 30.

	Isaiah	Lucy	Harris
Before	30x2 =  60 u	25x2 = 50 u	18x2 = 36 u
Change			+ 9x2 = + 18 u
Comparing the changes in the number of erasers	- 1x3 = - 3 u	- 5x3 = - 15 u	+ 6x3 = + 18 u
After	57 u	35 u	27x2 = 54 u

50% x 18 
= ⁵⁰₁₀₀ x 18 
= 9 

The total number of erasers that Isaiah and Lucy gave to Harris is repeated.  Make the total number of erasers that Isaiah and Lucy gave to Harris the same.  LCM of 6 and 9 is 18.

Number of erasers that Lucy had less than Harris 
= 54 u - 35 u
= 19 u

19 u = 171

1 u = 171 ÷ 19 = 9

Number of erasers that Lucy gave to Harris
= 15 u
= 15 x 9
= 135

Answer(s): 135