Abi and Ben collect cards and pencils. Ben has 45 less cards than pencils. Ben has 2 times the number of cards Abi has, and Abi has 40% more pencils than Ben. After Abi gives Ben all of her cards and Ben gives Abi 60% of his pencils, Ben has 15 more cards than pencils. Find the number of pencils Abi has at first.

Abi		Ben
Pencils	Cards	Pencils	Cards
2.8 u + 63	1 u	2 u + 45	2 u
+ 1.2 u + 27	- 1 u	- 1.2 u - 27	+ 1 u
4 u + 90	0	0.8 u + 18	3 u

100%+ 40% = 140% 

140% x 2 u
= ¹⁴⁰₁₀₀ x 2 u
= 2.8 u

140% x 45
= ¹⁴⁰₁₀₀ x 45
= 63 

60% x 2 u
= ⁶⁰₁₀₀ x 2 u
= 1.2 u  

60% x 45 
= ⁶⁰₁₀₀ x 45
= 27 

If another 15 pencils are given to Ben, he will have equal number of pencils and cards in the end.
3 u = 0.8 u + 18 + 15
3 u - 0.8 u = 33
2.2 u = 33

1 u = 33 ÷ 2.2 = 15

Number of pencils that Abi has at first
= 2.8 u + 63
= 2.8 x 15 + 63
= 42 + 63
= 105
 
Answer(s): 105