Vanessa and Tom collect pencils and buttons. Tom has 40 less pencils than buttons. Tom has 4 times the number of pencils Vanessa has, and Vanessa has 20% more buttons than Tom. After Vanessa gives Tom all of her pencils and Tom gives Vanessa 75% of his buttons, Tom has 70 less buttons than pencils. Find the number of buttons Vanessa has at first.

Vanessa		Tom
Buttons	Pencils	Buttons	Pencils
4.8 u + 48	1 u	4 u + 40	4 u
+ 3 u + 30	- 1 u	- 3 u - 30	+ 1 u
7.8 u + 78	0	1 u + 10	5 u

100%+ 20% = 120% 

120% x 4 u
= ¹²⁰₁₀₀ x 4 u
= 4.8 u

120% x 40
= ¹²⁰₁₀₀ x 40
= 48 

75% x 4 u
= ⁷⁵₁₀₀ x 4 u
= 3 u  

75% x 40 
= ⁷⁵₁₀₀ x 40
= 30 

If another 70 buttons are given to Tom, he will have equal number of buttons and pencils in the end.
5 u = 1 u + 10 + 70
5 u - 1 u = 80
4 u = 80

1 u = 80 ÷ 4 = 20

Number of buttons that Vanessa has at first
= 4.8 u + 48
= 4.8 x 20 + 48
= 96 + 48
= 144
 
Answer(s): 144