Let there be 
50 cent coins (call them halfs), 
10 cent coins (dimes) and 
5 cent coins (nickles).
81 coins:
Three more dimes than halfs:
Nickels are twice halfs plus dimes:
Three equations in three unknowns. We'll eliminate first:
Substituting
Check we have the right number of coins:
Good. The amount of money is
Part 2.
a for amount Tim gave cousin. Initially Tim has $146.65, cousin $10.55
After he gave the money Tim had twice as much:
That's the answer to b. After the transfer the cousin has
81 coins:
Three more dimes than halfs:
Nickels are twice halfs plus dimes:
Three equations in three unknowns. We'll eliminate
Substituting
Check we have the right number of coins:
Good. The amount of money is
Part 2.
a for amount Tim gave cousin. Initially Tim has $146.65, cousin $10.55
After he gave the money Tim had twice as much:
That's the answer to b. After the transfer the cousin has