Rachel and John collect cards and marbles. John has 100 more marbles than cards. John has 5 times the number of cards Rachel has, and Rachel has 30% more marbles than John. After Rachel gives John all of her cards and John gives Rachel 70% of his marbles, John has 51 more cards than marbles. Find the number of marbles Rachel has at first.

Rachel		John
Marbles	Cards	Marbles	Cards
6.5 u + 130	1 u	5 u + 100	5 u
+ 3.5 u + 70	- 1 u	- 3.5 u - 70	+ 1 u
10 u + 200	0	1.5 u + 30	6 u

100% + 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 100
= ¹³⁰₁₀₀ x 100
= 130 

70% x 5 u
= ⁷⁰₁₀₀ x 5 u
= 3.5 u  

70% x 100 
= ⁷⁰₁₀₀ x 100
= 70 

If another 51 marbles are given to John, he will have equal number of marbles and cards in the end.
6 u = 1.5 u + 30 + 51
6 u - 1.5 u = 81
4.5 u = 81

1 u = 81 ÷ 4.5 = 18

Number of marbles that Rachel has at first
= 6.5 u + 130
= 6.5 x 18 + 130
= 117 + 130
= 247
 
Answer(s): 247