Gem and Fabian collect pencils and erasers. Fabian has 60 more erasers than pencils. Fabian has 5 times the number of pencils Gem has, and Gem has 25% more erasers than Fabian. After Gem gives Fabian all of her pencils and Fabian gives Gem 60% of his erasers, Fabian has 24 more pencils than erasers. Find the number of erasers Gem has at first.

Gem		Fabian
Erasers	Pencils	Erasers	Pencils
6.25 u + 75	1 u	5 u + 60	5 u
+ 3 u + 36	- 1 u	- 3 u - 36	+ 1 u
9.25 u + 111	0	2 u + 24	6 u

100% + 25% = 125% 

125% x 5 u
= ¹²⁵₁₀₀ x 5 u
= 6.25 u

125% x 60
= ¹²⁵₁₀₀ x 60
= 75 

60% x 5 u
= ⁶⁰₁₀₀ x 5 u
= 3 u  

60% x 60 
= ⁶⁰₁₀₀ x 60
= 36 

If another 24 erasers are given to Fabian, he will have equal number of erasers and pencils in the end.
6 u = 2 u + 24 + 24
6 u - 2 u = 48
4 u = 48

1 u = 48 ÷ 4 = 12

Number of erasers that Gem has at first
= 6.25 u + 75
= 6.25 x 12 + 75
= 75 + 75
= 150
 
Answer(s): 150