Since we have different fractions, we can try to find a common denominator which will make our calculations easier. Since 8 x 7 = 56, I’ll use 56 as the denominator.

Total: 56/56 or 56 units

Given to friends: 3/8 x 56 units
= 21 units

Remainder after giving friends: 56 units – 21 units
= 35 units

Given to brother: 5/7 x 35 units = 25 units

Remainder after giving friends and brother: 56 units – 21 units – 25 units
= 10 units

We know that his cousin gave him 408 marbles ( 10 units + 408) and he ended up with twice the number of marbles he had at first (56 units x 2). Therefore,

10 units + 408 = 56 units x 2
10 units + 408 = 112 units
112 units – 10 units = 408
102 units = 408
1 unit = 408 ÷ 102
= 4
56 units = 56 x 4
= 224 marbles at first

Thank you sooo much for the solution and explaination