Gem and Fred collect pens and erasers. Fred has 35 less pens than erasers. Fred has 3 times the number of pens Gem has, and Gem has 40% more erasers than Fred. After Gem gives Fred all of her pens and Fred gives Gem 60% of his erasers, Fred has 42 less erasers than pens. Find the number of erasers Gem has at first.

Gem		Fred
Erasers	Pens	Erasers	Pens
4.2 u + 49	1 u	3 u + 35	3 u
+ 1.8 u + 21	- 1 u	- 1.8 u - 21	+ 1 u
6 u + 70	0	1.2 u + 14	4 u

100%+ 40% = 140% 

140% x 3 u
= ¹⁴⁰₁₀₀ x 3 u
= 4.2 u

140% x 35
= ¹⁴⁰₁₀₀ x 35
= 49 

60% x 3 u
= ⁶⁰₁₀₀ x 3 u
= 1.8 u  

60% x 35 
= ⁶⁰₁₀₀ x 35
= 21 

If another 42 erasers are given to Fred, he will have equal number of erasers and pens in the end.
4 u = 1.2 u + 14 + 42
4 u - 1.2 u = 56
2.8 u = 56

1 u = 56 ÷ 2.8 = 20

Number of erasers that Gem has at first
= 4.2 u + 49
= 4.2 x 20 + 49
= 84 + 49
= 133
 
Answer(s): 133