document.write( "Question 871606: A coin collection contains 29 coins. It consists of pennies, nickels, and quarters. The number of quarters is 4 fewer than the number of nickels, and the face value of the collection is $2.69. How many of each denomination are there in the collection? \n" ); document.write( "

Algebra.Com's Answer #525637 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+p+\"$ = number of pennies
\n" ); document.write( "Let $\"+n+\"$ = number of nickels
\n" ); document.write( "Let $\"+q+\"$ = number of quarters
\n" ); document.write( "----------------------------
\n" ); document.write( "(1) $\"+p+%2B+n+%2B+q+=+29+\"$
\n" ); document.write( "(2) $\"+q+=+n+-+4+\"$
\n" ); document.write( "(3) $\"+1%2Ap+%2B+5n+%2B+25q+=+269+\"$ ( in cents )
\n" ); document.write( "-------------------------------------
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+p+%2B+n+%2B+n+-+4+=+29+\"$
\n" ); document.write( "(1) $\"+p+%2B+2n+=+33+\"$
\n" ); document.write( "(1) $\"+p+=+-2n+%2B+33+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Substitute (1) and (2) into (3)
\n" ); document.write( "(3) $\"+1%2Ap+%2B+5n+%2B+25q+=+269+\"$
\n" ); document.write( "(3) $\"+1%2A%28+-2n+%2B+33+%29+%2B+5n+%2B+25%2A%28+n-4+%29+=+269+\"$
\n" ); document.write( "(3) $\"+-2n+%2B+33+%2B+5n+%2B+25n+-+100+=+269+\"$
\n" ); document.write( "(3) $\"+28n+=+269+%2B+67+\"$
\n" ); document.write( "(3) $\"+28n+=+336+\"$
\n" ); document.write( "(3) $\"+n+=+12+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+q+=+n+-+4+\"$
\n" ); document.write( "(2) $\"+q+=+12+-+4+\"$
\n" ); document.write( "(2) $\"+q+=+8+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+p+=+-2n+%2B+33+\"$
\n" ); document.write( "(1) $\"+p+=+-2%2A12+%2B+33+\"$
\n" ); document.write( "(1) $\"+p+=+-24+%2B+33+\"$
\n" ); document.write( "(1) $\"+p+=+9+\"$
\n" ); document.write( "There are 9 pennies, 12 nickels, and 8 quarters
\n" ); document.write( "-------------
\n" ); document.write( "check:
\n" ); document.write( "(3) $\"+1%2Ap+%2B+5n+%2B+25q+=+269+\"$
\n" ); document.write( "(3) $\"+1%2A9+%2B+5%2A12+%2B+25%2A8+=+269+\"$
\n" ); document.write( "(3) $\"+9+%2B+60+%2B+200+=+269+\"$
\n" ); document.write( "(3) $\"+269+=+269+\"$
\n" ); document.write( "OK
\n" ); document.write( "(1) $\"+p+%2B+n+%2B+q+=+29+\"$
\n" ); document.write( "(1) $\"+9+%2B+12+%2B+8+=+29+\"$
\n" ); document.write( "(1) $\"+29+=+29+\"$
\n" ); document.write( "OK
\n" ); document.write( "(2) $\"+q+=+n+-+4+\"$
\n" ); document.write( "(2) $\"+8+=+12+-+4+\"$
\n" ); document.write( "(2) $\"+8+=+8+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );