Betty and Fred collect beads and pencils. Fred has 80 less beads than pencils. Fred has 5 times the number of beads Betty has, and Betty has 30% more pencils than Fred. After Betty gives Fred all of her beads and Fred gives Betty 75% of his pencils, Fred has 75 more beads than pencils. Find the number of pencils Betty has at first.

Betty		Fred
Pencils	Beads	Pencils	Beads
6.5 u + 104	1 u	5 u + 80	5 u
+ 3.75 u + 60	- 1 u	- 3.75 u - 60	+ 1 u
10.25 u + 164	0	1.25 u + 20	6 u

100%+ 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 80
= ¹³⁰₁₀₀ x 80
= 104 

75% x 5 u
= ⁷⁵₁₀₀ x 5 u
= 3.75 u  

75% x 80 
= ⁷⁵₁₀₀ x 80
= 60 

If another 75 pencils are given to Fred, he will have equal number of pencils and beads in the end.
6 u = 1.25 u + 20 + 75
6 u - 1.25 u = 95
4.75 u = 95

1 u = 95 ÷ 4.75 = 20

Number of pencils that Betty has at first
= 6.5 u + 104
= 6.5 x 20 + 104
= 130 + 104
= 234
 
Answer(s): 234