Rachel had 40% more erasers than Wyatt. Rael had 20% fewer erasers than Rachel. Rachel and Wyatt gave Rael some erasers in the ratio of 1 : 3. As a result, Rael had 50% more erasers than before. Given that Wyatt had 330 less erasers than Rael in the end, how many erasers did Wyatt give to Rael?

Rachel	Wyatt	Rael
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Rachel : Wyatt = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Rachel : Rael = 5 : 4

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

	Rachel	Wyatt	Rael
Before	35x2 =  70 u	25x2 = 50 u	28x2 = 56 u
Change			+ 14x2 = + 28 u
Comparing the changes in the number of erasers	- 1x7 = - 7 u	- 3x7 = - 21 u	+ 4x7 = + 28 u
After	63 u	29 u	42x2 = 84 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of erasers that Rachel and Wyatt gave to Rael is repeated.  Make the total number of erasers that Rachel and Wyatt gave to Rael the same.  LCM of 4 and 14 is 28.

Number of erasers that Wyatt had less than Rael 
= 84 u - 29 u
= 55 u

55 u = 330

1 u = 330 ÷ 55 = 6

Number of erasers that Wyatt gave to Rael
= 21 u
= 21 x 6
= 126

Answer(s): 126