There can only be an odd number of $50 bills, because if you
had an even number of $50 bills, they would amount to
$100, which would leave $410 to make with $20 bils only, which
is impossible, or
$200, which would leave $310 to make with $20 bils only, which
is impossible, or
$300, which would leave $210 to make with $20 bils only, which
is impossible, or
$400, which would leave $110 to make with $20 bils only, which
is impossible, or
$500, which would leave $10 to make with $20 bils only, which
is impossible.
But if you had an odd number of $50 bills, they would amount to
1. 1 fifty, or $50, which would leave $460 to make with $20 bills
only, which can be made with 23 $20 bills.
2. 3 fifties, or $150, which would leave $360 to make with $20 bills only, which can be made with 18 $20 bills.
3. 5 fifties, or $250, which would leave $260 to make with $20 bills only, which can be made with 13 $20 bills.
4. 7 fifties, or $350, which would leave $160 to make with $20 bills only, which can be made with 8 $20 bills.
5. 9 fifties, or $450, which would leave $60 to make with $20 bills only,
which can be made with 3 $20 bills.
So there are 5 possible denominations of $20 and $50 that sum up to $510.
Edwin
