document.write( "Question 600618: lynn has 159$ in her purse consisting of 20, 5 and 1s'. the number of 20s is the same as the 1s and 5s if she has 14 bills how many of each does she have? \n" ); document.write( "

Algebra.Com's Answer #379402 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of 1's
\n" ); document.write( "Let $\"+b+\"$ = number of 5's
\n" ); document.write( "Let $\"+c+\"$ = number of 20's
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+c+=+a+%2B+b+\"$
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+c+=+14+\"$
\n" ); document.write( "(3) $\"+1a+%2B+5b+%2B+20c+=+159+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "Substitute (1) into (2) and
\n" ); document.write( "(1) into (3)
\n" ); document.write( "(2) $\"+a+%2B+b+%2B+a+%2B+b+=+14+\"$
\n" ); document.write( "(2) $\"+2a+%2B+2b+=+14+\"$
\n" ); document.write( "(2) $\"+a+%2B+b+=+7+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+1a+%2B+5b+%2B+20%2A%28+a+%2B+b+%29+=+159+\"$
\n" ); document.write( "(3) $\"+1a+%2B+5b+%2B+20a+%2B+20b+%29+=+159+\"$
\n" ); document.write( "(3) $\"+21a+%2B+25b+=+159+\"$
\n" ); document.write( "Multiply both sides of (2) by $\"+21+\"$
\n" ); document.write( "and subtract (2) from (3)
\n" ); document.write( "(3) $\"+21a+%2B+25b+=+159+\"$
\n" ); document.write( "(2) $\"+-21a+-+21b+=+147+\"$
\n" ); document.write( " $\"+4b+=+12+\"$
\n" ); document.write( " $\"+b+=+3+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+a+%2B+b+=+7+\"$
\n" ); document.write( "(2) $\"+a+%2B+3+=+7+\"$
\n" ); document.write( "(2) $\"+a+=+4+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+c+=+a+%2B+b+\"$
\n" ); document.write( "(1) $\"+c+=+4+%2B+3+\"$
\n" ); document.write( "(1) $\"+c+=+7+\"$
\n" ); document.write( "She has 4 ones, 3 fives, and 7 twenties
\n" ); document.write( "check:
\n" ); document.write( "(3) $\"+1a+%2B+5b+%2B+20c+=+159+\"$
\n" ); document.write( "(3) $\"+1%2A4+%2B+5%2A3+%2B+20%2A7+=+159+\"$
\n" ); document.write( "(3) $\"+4+%2B+15+%2B+140+=+159+\"$
\n" ); document.write( "(3) $\"+159+=+159+\"$
\n" ); document.write( "OK \n" ); document.write( "

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