Question 801574
<pre>
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</pre>