Question 947502
u, f, t, how many of the "units", fives, and tens.


No more than ten bills, means {{{u+f+t<=10}}}.  Might start first with the equality of this.


Amount of change will be $27, so  {{{u+5f+10t=27}}}.


The best way to find all the combinations is to form tree-diagrams, not to try any simultaneous equations.  Start with the most efficient combination first, and then work from there to make the less efficient combinations.  The most efficient bill combination is  t=2, f=1, u=2.
Next, split the f into five of the units, so have t=2, f=0, u=2+5=7.


Continue looking for more ways to split more of the bills...


I did not finish this, but only described how to find the combinations.