Diana and Valen collect erasers and marbles. Valen has 30 less erasers than marbles. Valen has 2 times the number of erasers Diana has, and Diana has 40% more marbles than Valen. After Diana gives Valen all of her erasers and Valen gives Diana 70% of his marbles, Valen has 39 less marbles than erasers. Find the number of marbles Diana has at first.

Diana		Valen
Marbles	Erasers	Marbles	Erasers
2.8 u + 42	1 u	2 u + 30	2 u
+ 1.4 u + 21	- 1 u	- 1.4 u - 21	+ 1 u
4.2 u + 63	0	0.6 u + 9	3 u

100%+ 40% = 140% 

140% x 2 u
= ¹⁴⁰₁₀₀ x 2 u
= 2.8 u

140% x 30
= ¹⁴⁰₁₀₀ x 30
= 42 

70% x 2 u
= ⁷⁰₁₀₀ x 2 u
= 1.4 u  

70% x 30 
= ⁷⁰₁₀₀ x 30
= 21 

If another 39 marbles are given to Valen, he will have equal number of marbles and erasers in the end.
3 u = 0.6 u + 9 + 39
3 u - 0.6 u = 48
2.4 u = 48

1 u = 48 ÷ 2.4 = 20

Number of marbles that Diana has at first
= 2.8 u + 42
= 2.8 x 20 + 42
= 56 + 42
= 98
 
Answer(s): 98