Question 274991
Let {{{q}}} = number of quarters
Let {{{h}}} = number of half dollars
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given:
(1)  {{{h + q = 21}}}
(2) {{{50h + 25q = 650}}} (in cents)
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Multiply both sides of (1) by {{{25}}}
and subtract from (2)
(2) {{{50h + 25q = 650}
(1) {{{-25h - 25q = 525}}}
{{{25h = 125}}}
{{{h = 5}}}
And, since
(1)  {{{h + q = 21}}}
{{{5 + q = 21}}}
{{{q = 16}}}
There are 16 quarters and 5 half dollars
check:
(2) {{{50h + 25q = 650}}}
{{{50*5 + 25*16 = 650}}}
{{{250 + 400 = 650}}}
{{{650 = 650}}}
OK