Question 274250
Let {{{n}}} = number of nickels
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
{{{n + d + q = 24}}}
{{{5n + 10d + 25q = 200}}}
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{{{8*25 = 200}}}
{{{n + d + q = 8}}}
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{{{7*25 = 175}}}
{{{5n = 25}}}
{{{n + d + q = 12}}}
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{{{6*25 = 150}}}
{{{10*5 = 50}}}
{{{n + d + q = 16}}}
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{{{5*25 = 125}}}
{{{15*5 = 75}}}
{{{n + d + q = 20}}}
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{{{4*25 = 100}}}
{{{20*5 = 100}}}
{{{n + d + q = 24}}} 
4 quarters and 20 nickels
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{{{2*25 = 50}}}
{{{n + d + 2 = 24}}}
{{{d = 22 - n}}}
{{{5n + 10d + 50 = 200}}}
{{{5n + 10*(22-n) + 50 = 200}}}
{{{5n + 220 - 10n + 50 = 200}}}
{{{5n = 270 - 200}}}
{{{5n = 70}}}
{{{n = 14}}}
and
{{{d = 22-n}}}
{{{d = 22 - 14}}}
{{{d = 8}}}
2 quarters, 14 nickels, and 8 dimes