document.write( "Question 884303: John has 27 coins totaling $5.70. If he only has dimes and quarters, how many of each coin does he have? \n" ); document.write( "

Algebra.Com's Answer #534166 by josmiceli(19441) $\"\"$ $\"About$

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(a) He can't have an odd number of quarters,
\n" ); document.write( "since that would make the total look like @@.@5
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\n" ); document.write( "(b) He can't have 23 or more quarters, since
\n" ); document.write( "that is $5.75 or greater
\n" ); document.write( "-----------------------
\n" ); document.write( "Let $\"+d+\"$ = number of dimes he has
\n" ); document.write( "Let $\"+q+\"$ = number of quarters he has
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\n" ); document.write( "(1) $\"+d+%2B+q+=+27+\"$
\n" ); document.write( "(2) $\"+10d+%2B+25q+=+570+\"$ ( in cents )
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\n" ); document.write( "Multiply both sides of (1) by $\"+10+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+10d+%2B+25q+=+570+\"$
\n" ); document.write( "(1) $\"+-10d+-+10q+=+-270+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( " $\"+15q+=+300+\"$
\n" ); document.write( " $\"+q+=+20+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+d+%2B+q+=+27+\"$
\n" ); document.write( "(1) $\"+d+%2B+20+=+27+\"$
\n" ); document.write( "(1) $\"+d+=+7+\"$
\n" ); document.write( "He has 7 dimes and 20 quarters
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+10%2A7+%2B+25%2A20+=+570+\"$
\n" ); document.write( "(2) $\"+70+%2B+500+=+570+\"$
\n" ); document.write( "(2) $\"+570+=+570+\"$
\n" ); document.write( "OK
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