Emma and Cody collect cards and pencils. Cody has 35 more pencils than cards. Cody has 4 times the number of cards Emma has, and Emma has 40% more pencils than Cody. After Emma gives Cody all of her cards and Cody gives Emma 60% of his pencils, Cody has 54 more cards than pencils. Find the number of pencils Emma has at first.

Emma		Cody
Pencils	Cards	Pencils	Cards
5.6 u + 49	1 u	4 u + 35	4 u
+ 2.4 u + 21	- 1 u	- 2.4 u - 21	+ 1 u
8 u + 70	0	1.6 u + 14	5 u

100% + 40% = 140% 

140% x 4 u
= ¹⁴⁰₁₀₀ x 4 u
= 5.6 u

140% x 35
= ¹⁴⁰₁₀₀ x 35
= 49 

60% x 4 u
= ⁶⁰₁₀₀ x 4 u
= 2.4 u  

60% x 35 
= ⁶⁰₁₀₀ x 35
= 21 

If another 54 pencils are given to Cody, he will have equal number of pencils and cards in the end.
5 u = 1.6 u + 14 + 54
5 u - 1.6 u = 68
3.4 u = 68

1 u = 68 ÷ 3.4 = 20

Number of pencils that Emma has at first
= 5.6 u + 49
= 5.6 x 20 + 49
= 112 + 49
= 161
 
Answer(s): 161