Kaylee had 25% more erasers than Natalie. Joshua had 50% fewer erasers than Kaylee. Kaylee and Natalie gave Joshua some erasers in the ratio of 4 : 5. As a result, Joshua had 60% more erasers than before. Given that Natalie had 15 less erasers than Joshua in the end, how many erasers did Natalie give to Joshua?

Kaylee	Natalie	Joshua
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Kaylee : Natalie = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Kaylee : Joshua = 2 : 1

The number of erasers that Kaylee had at first is repeated. Make the number of erasers that Kaylee had at first the same.  LCM of 5 and 2 is 10.

	Kaylee	Natalie	Joshua
Before	10x3 =  30 u	8x3 = 24 u	5x3 = 15 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of erasers	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	26 u	19 u	8x3 = 24 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of erasers that Kaylee and Natalie gave to Joshua is repeated.  Make the total number of erasers that Kaylee and Natalie gave to Joshua the same.  LCM of 9 and 3 is 9.

Number of erasers that Natalie had less than Joshua 
= 24 u - 19 u
= 5 u

5 u = 15

1 u = 15 ÷ 5 = 3

Number of erasers that Natalie gave to Joshua
= 5 u
= 5 x 3
= 15

Answer(s): 15