Question 1207307
<pre>
BILL      VALUE-FACE         VARIABLE      MONEY
Ten       10                    x          10x
Fove       5                    y           5y
Two        2                    z           2z
TOTAL                                      67

And,  {{{x+y+z=13}}}, for 13 pieces
{{{10x+5y+2z=67}}}, for amount of money.
</pre>

Eliminate z, to have a single equation in x and y.

{{{system(2x+2y+2z=26,10x+5y+2z=67)}}}


{{{8x+3y=41}}}---------find some meaningful whole value combinations for x and y.

{{{3y=-8x+41}}}
{{{y=-(8/3)x+41/3}}}
(1,11)
(4,3)


What happens to z for either of those two x & y pair?
Either (1,11,1)  or  (4,3,6).


How is the money quantity with each of those?
{{{10*1+5*11+2*1=67}}}----A Match!
-
{{{10*4+5*3+2*6}}}-----also match!


RESULT:
One of $10 bill
Eleven of $5 bill
One of $2 bill


Also 
four of $10
three of $5
six of $2