Question

Seth had some marbles. He gave 2/3 of his marbles to Henry and bought 4 new marbles. After that, he gave 2/7 of his remaining marbles to his cousin and bought another 7 new marbles. In the end, Seth had 47 marbles. How many marbles did Seth give to his cousin? How many marbles did Seth have at first?

Answer 1

Let the initial quantity of marble = X
Then, the number of marbles given to Henry = (2/3) * X
Now,
Quantity of marbles left with Seth = (X - (2/3) * X)
Quantity of marbles left with Seth = (1/3) * X
After adding 4 marbles,
The new level of quantity of marbles left with Seth = (1/3) * X + 4
Now 2/7 of the new level of quantity is given to cousin, then
The remaining quantity of marble with Seth = ((1/3) * X + 4) - (2/7) * ((1/3) * X + 4)
Now 7 new marbles are added, then:
Final quantity = 47
((1/3 * X + 4) - (2/7) * ((1/3) * X + 4) + 7 = 47
((1/3 * X + 4) - (2/7) * ((1/3) * X + 4) = 47 - 7
40 = ((1/3) * X - (2/21) * X + 4 - (2/7) * 4
X = (40 - 4 + (2/7) * 4) / ((1/3) - (2/21))
X = 156
So,
Number of marbles given to cousin =
(2/7) * ((1/3) * 156 + 4)
Number of marbles given to cousin = 16
And,
Number of marbles with Seth at first = 156

Hence the correct answer:
Number of marbles given to cousin = 16
Number of marbles with Seth at first = 156