Question 108480
These kind of problems require that you deal both with the number of coins and their value.  Knowing that there are 40 total coins allows us to write:
:
{{{d + n=40}}}
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Knowing that there are 10 cents in each dime, 5 cents in each nickel, and a total of 290 cents ($2.90) in value for the 40 coins, we can write:
:
{{{10d+5n=290}}}
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but since {{{d=40-n}}}, we can substitute:
:
{{{10(40-n)+5n = 290}}}
{{{400-10n+5n=290}}}
{{{-5n=-110}}}
{{{n=22}}}
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Meaning that there are 22 nickels worth $1.10.
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To check your answer, note that there are {{{40-22=18}}} dimes. And 18 dimes are worth, $1.80.  {{{1.80 + 1.10 = 2.90}}}