Diana and Warren collect pencils and marbles. Warren has 50 less pencils than marbles. Warren has 4 times the number of pencils Diana has, and Diana has 30% more marbles than Warren. After Diana gives Warren all of her pencils and Warren gives Diana 70% of his marbles, Warren has 61 less marbles than pencils. Find the number of marbles Diana has at first.

Diana		Warren
Marbles	Pencils	Marbles	Pencils
5.2 u + 65	1 u	4 u + 50	4 u
+ 2.8 u + 35	- 1 u	- 2.8 u - 35	+ 1 u
8 u + 100	0	1.2 u + 15	5 u

100%+ 30% = 130% 

130% x 4 u
= ¹³⁰₁₀₀ x 4 u
= 5.2 u

130% x 50
= ¹³⁰₁₀₀ x 50
= 65 

70% x 4 u
= ⁷⁰₁₀₀ x 4 u
= 2.8 u  

70% x 50 
= ⁷⁰₁₀₀ x 50
= 35 

If another 61 marbles are given to Warren, he will have equal number of marbles and pencils in the end.
5 u = 1.2 u + 15 + 61
5 u - 1.2 u = 76
3.8 u = 76

1 u = 76 ÷ 3.8 = 20

Number of marbles that Diana has at first
= 5.2 u + 65
= 5.2 x 20 + 65
= 104 + 65
= 169
 
Answer(s): 169