document.write( "Question 190775: Elisa has $151 in her wallet, consisting of $20, $5, and $1 bills. The number of $20 bills is three less than the number of $5 bills. If she has 24 bills in her wallet, how many of each denomination does she have? \n" ); document.write( "

Algebra.Com's Answer #143224 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = the number of $1 bills
\n" ); document.write( "Let $\"b\"$ = the number of $5 bills
\n" ); document.write( "Let $\"c\"$ = the number of $20 bills
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"c+=+b+-+3\"$
\n" ); document.write( "(2) $\"a+%2B+b+%2B+c+=+24\"$
\n" ); document.write( "(3) $\"1a+%2B+5b+%2B+20c+=+151\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "Subtract (2) from (3)
\n" ); document.write( " $\"4b+%2B+19c+=+127\"$
\n" ); document.write( "Substitute $\"c\"$ in (1)
\n" ); document.write( " $\"4b+%2B+19%2A%28b+-+3%29+=+127\"$
\n" ); document.write( " $\"4b+%2B+19b+-+57+=+127\"$
\n" ); document.write( " $\"23b+=+184\"$
\n" ); document.write( " $\"b+=+8\"$
\n" ); document.write( "and, from (1)
\n" ); document.write( " $\"c+=+8+-+3\"$
\n" ); document.write( " $\"c+=+5\"$
\n" ); document.write( "And using (2)
\n" ); document.write( " $\"a+%2B+b+%2B+c+=+24\"$
\n" ); document.write( " $\"a+%2B+8+%2B+5+=+24\"$
\n" ); document.write( " $\"a+=+11\"$
\n" ); document.write( "She has 11 $1 bills, 8 $5 bills, and 5 $20 bills
\n" ); document.write( "check answer:
\n" ); document.write( "(3) $\"1a+%2B+5b+%2B+20c+=+151\"$
\n" ); document.write( " $\"11+%2B+5%2A8+%2B+20%2A5+=+151\"$
\n" ); document.write( " $\"11+%2B+40+%2B+100+=+151\"$
\n" ); document.write( " $\"151+=+151\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );