Question 51636
We have two equations:  {{{q+d=40}}} represents the number of q quarters and d dimes, and {{{.25q+.10d=4.90}}} represents the total value of the 40 coins.  Solving for d in the first equation yields {{{d=40-q}}} and we substitute that into the second equation for d:  {{{.25q+.10*(40-q)=4.90}}}.  Expanding this latest equation produces {{{.25q+4-.10q=4.90}}}.  Now combine like terms:  {{{.15q+4=4.90}}}.  Subtracting 4 from each side produces: {{{.15q=.90}}}.  And now divide both sides by .15 yields {{{q=6}}}.  That means there are 6 quarters.  Because we know there are 40 coins total, there must be 40-6, or 34, dimes.  To verify that answer, 34 dimes is $3.40 and 6 quarters is $1.50.  Adding those two values together produces $4.90, which means our answer of 6 quarters and 34 dimes is correct.