Question 130316
Let's say we have n nickels and d dimes.  That means that:


{{{n + d = 304}}}, because that is the number of coins we have altogether.


A nickel is worth 5 cents, so the value of all of the nickels is 5n cents.  Likewise, the value of all of the dimes is 10d.


Just because I don't like mucking about with decimal coefficients, let's change the total amount of money from $22.40 to 2240 cents.


Now we can say that {{{5n+10d=2240}}}


We can re-state the first equation by solving it for either of the variables.  Let's solve it for d:  {{{d=304-n}}}


Now take this expression for d and substitute it into the second equation:


{{{5n+10(304-n)=2240}}}


{{{5n-10n+3040=2240}}}


{{{-5n=2240-3040}}}


{{{-5n=-800}}}


{{{n=160}}}


So there were 160 nickels.


Check the answer.


If there were 160 nickels, then there were 144 dimes (304 - 160).  144 dimes is $14.40,  160 nickels is $8.00.  $14.40 + $8.00 = $22.40.  Answer checks.