Natalie and Fred collect erasers and beads. Fred has 60 less erasers than beads. Fred has 4 times the number of erasers Natalie has, and Natalie has 40% more beads than Fred. After Natalie gives Fred all of her erasers and Fred gives Natalie 70% of his beads, Fred has 39 less beads than erasers. Find the number of beads Natalie has at first.

Natalie		Fred
Beads	Erasers	Beads	Erasers
5.6 u + 84	1 u	4 u + 60	4 u
+ 2.8 u + 42	- 1 u	- 2.8 u - 42	+ 1 u
8.4 u + 126	0	1.2 u + 18	5 u

100%+ 40% = 140% 

140% x 4 u
= ¹⁴⁰₁₀₀ x 4 u
= 5.6 u

140% x 60
= ¹⁴⁰₁₀₀ x 60
= 84 

70% x 4 u
= ⁷⁰₁₀₀ x 4 u
= 2.8 u  

70% x 60 
= ⁷⁰₁₀₀ x 60
= 42 

If another 39 beads are given to Fred, he will have equal number of beads and erasers in the end.
5 u = 1.2 u + 18 + 39
5 u - 1.2 u = 57
3.8 u = 57

1 u = 57 ÷ 3.8 = 15

Number of beads that Natalie has at first
= 5.6 u + 84
= 5.6 x 15 + 84
= 84 + 84
= 168
 
Answer(s): 168