Nora and Ian collect beads and marbles. Ian has 40 less beads than marbles. Ian has 5 times the number of beads Nora has, and Nora has 30% more marbles than Ian. After Nora gives Ian all of her beads and Ian gives Nora 75% of his marbles, Ian has 9 more beads than marbles. Find the number of marbles Nora has at first.

Nora		Ian
Marbles	Beads	Marbles	Beads
6.5 u + 52	1 u	5 u + 40	5 u
+ 3.75 u + 30	- 1 u	- 3.75 u - 30	+ 1 u
10.25 u + 82	0	1.25 u + 10	6 u

100%+ 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 40
= ¹³⁰₁₀₀ x 40
= 52 

75% x 5 u
= ⁷⁵₁₀₀ x 5 u
= 3.75 u  

75% x 40 
= ⁷⁵₁₀₀ x 40
= 30 

If another 9 marbles are given to Ian, he will have equal number of marbles and beads in the end.
6 u = 1.25 u + 10 + 9
6 u - 1.25 u = 19
4.75 u = 19

1 u = 19 ÷ 4.75 = 4

Number of marbles that Nora has at first
= 6.5 u + 52
= 6.5 x 4 + 52
= 26 + 52
= 78
 
Answer(s): 78