document.write( "Question 718478: You find 6 coins in an old desk drawer, consisting entirely of nickels, dimes, and quarters, with a face value of 85 cents. However, the coins all date from 1889 and are worth much more than their face value, and you were able to sell all the coins to a coin shop for a total of $31. Suppose you received $5 for each nickel, $4 for each dime, and $7 for each quarter. How many of the coins were quarters? \n" ); document.write( "

Algebra.Com's Answer #440947 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+q+\"$ = number of quarters
\n" ); document.write( "Let $\"+d+\"$ = number of dimes
\n" ); document.write( "Let $\"+n+\"$ = number of nickels
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+n+%2B+d+%2B+q+=+6+\"$
\n" ); document.write( "(2) $\"+5n+%2B+10d+%2B+25q+=+85+\"$ ( in cents )
\n" ); document.write( "(3) $\"+500n+%2B+400d+%2B+700q+=+3100+\"$ ( in cents )
\n" ); document.write( "------------------------------
\n" ); document.write( "There are 3 equations and 3 unknowns, so
\n" ); document.write( "it's solvable
\n" ); document.write( "Multiply both sides of (1) by $\"+400+\"$
\n" ); document.write( "and subtract (1) from (3)
\n" ); document.write( "---------------------
\n" ); document.write( "(3) $\"+500n+%2B+400d+%2B+700q+=+3100+\"$
\n" ); document.write( "(1) $\"+-400n+-+400d+-+400q+=+-2400+\"$
\n" ); document.write( " $\"+100n+%2B+300q+=+700+\"$
\n" ); document.write( " $\"+n+%2B+3q+=+7+\"$
\n" ); document.write( "--------------
\n" ); document.write( "Multiply both sides of (1) by $\"+10+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+5n+%2B+10d+%2B+25q+=+85+\"$
\n" ); document.write( "(1) $\"+-10n+-+10d+-+10q+=+-60+\"$
\n" ); document.write( " $\"+-5n+%2B+15q+=+25+\"$
\n" ); document.write( " $\"+-n+%2B+3q+=+5+\"$
\n" ); document.write( "----------------
\n" ); document.write( "Add the results of these 2 operations:
\n" ); document.write( " $\"+n+%2B+3q+=+7+\"$
\n" ); document.write( " $\"+-n+%2B+3q+=+5+\"$
\n" ); document.write( " $\"+6q+=+12+\"$
\n" ); document.write( " $\"+q+=+2+\"$
\n" ); document.write( "Two of the coins were quarters
\n" ); document.write( "check answer:
\n" ); document.write( " $\"+-n+%2B+3q+=+5+\"$
\n" ); document.write( " $\"+-n+%2B+3%2A2+=+5+\"$
\n" ); document.write( " $\"+-n+=+-1+\"$
\n" ); document.write( " $\"+n+=+1+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+n+%2B+d+%2B+q+=+6+\"$
\n" ); document.write( "(1) $\"+1+%2B+d+%2B+2+=+6+\"$
\n" ); document.write( "(1) $\"+d+=+3+\"$
\n" ); document.write( "-------------
\n" ); document.write( "(3) $\"+500n+%2B+400d+%2B+700q+=+3100+\"$
\n" ); document.write( "(3) $\"+5n+%2B+4d+%2B+7q+=+31+\"$
\n" ); document.write( "(3) $\"+5%2A1+%2B+4%2A3+%2B+7%2A2+=+31+\"$
\n" ); document.write( "(3) $\"+5+%2B+12+%2B+14+=+31+\"$
\n" ); document.write( "(3) $\"+31+=+31+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );