document.write( "Question 803271: michael has 58 coins totaling $4.40 all nickels dimes and quarters. the number of nickels is 2 short of being 3 times the sum of the number of dimes and quarters together how many dimes are there \n" ); document.write( "

Algebra.Com's Answer #484215 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+n+\"$ = number of nickels
\n" ); document.write( "Let $\"+d+\"$ = number of dimes
\n" ); document.write( "Let $\"+q+\"$ = number of quarters
\n" ); document.write( "----------------------------
\n" ); document.write( "(1) $\"+n+%2B+d+%2B+q+=+58+\"$
\n" ); document.write( "(2) $\"+5n+%2B+10d+%2B+25q+=+440+\"$ ( in cents )
\n" ); document.write( "(3) $\"+n+=+3%2A%28+d+%2B+q+%29+-+2+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "(3) $\"+n+=+3d+%2B+3q+-+2+\"$
\n" ); document.write( "(3) $\"+-n+%2B+3d+%2B+3q+=+2+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+-3+\"$
\n" ); document.write( "and add (1) and (3)
\n" ); document.write( "(1) $\"+-3n+-+3d+-+3q+=+-174+\"$
\n" ); document.write( "(3) $\"+-n+%2B+3d+%2B+3q+=+2+\"$
\n" ); document.write( " $\"+-4n+=+-172+\"$
\n" ); document.write( " $\"+n+=+43+\"$
\n" ); document.write( "-----------
\n" ); document.write( "(2) $\"+5%2A43+%2B+10d+%2B+25q+=+440+\"$
\n" ); document.write( "(2) $\"+10d+%2B+25q+=+440+-+215+\"$
\n" ); document.write( "(2) $\"+10d+%2B+25q+=+225+\"$
\n" ); document.write( "(2) $\"+2d+%2B+5q+=+45+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+-n+%2B+3d+%2B+3q+=+2+\"$
\n" ); document.write( "(3) $\"+3d+%2B+3q+=+43+%2B+2+\"$
\n" ); document.write( "(3) $\"+d+%2B+q+=+15+\"$
\n" ); document.write( "(3) $\"+2d+%2B+2q+=+30+\"$
\n" ); document.write( "Subtract (3) from (2)
\n" ); document.write( "(2) $\"+2d+%2B+5q+=+45+\"$
\n" ); document.write( "(3) $\"+-2d+-+2q+=+-30+\"$
\n" ); document.write( " $\"+3q+=+15+\"$
\n" ); document.write( " $\"+q+=+5+\"$
\n" ); document.write( "----------
\n" ); document.write( "(1) $\"+n+%2B+d+%2B+q+=+58+\"$
\n" ); document.write( "(1) $\"+43+%2B+d+%2B+5+=+58+\"$
\n" ); document.write( "(1) $\"+d+=+58+-+48+\"$
\n" ); document.write( "(1) $\"+d+=+10+\"$
\n" ); document.write( "There are 10 dimes
\n" ); document.write( "-----------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+5n+%2B+10d+%2B+25q+=+440+\"$
\n" ); document.write( "(2) $\"+5%2A43+%2B+10%2A10+%2B+25%2A5+=+440+\"$
\n" ); document.write( "(2) $\"+215+%2B+100+%2B+125+=+440+\"$
\n" ); document.write( "(2) $\"+440+=+440+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );