document.write( "Question 591482: A jar of change has $57.25 in it. There are 2 dimes more than 3 times the amount of nickels and 3 quarters less than double the amount of nickels. How many nickels, dimes, and quarters are in the jar? (There are no pennies!). How would I solve this problem? \n" ); document.write( "

Algebra.Com's Answer #375624 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+n+\"$ = number of nickels
\n" ); document.write( "Let $\"+d+\"$ = number of dimes
\n" ); document.write( "Let $\"+q+\"$ = number of quarters
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+5n+%2B+10d+%2B+25q+=+5725+\"$ ( in change )
\n" ); document.write( "(2) $\"+d+=+3n+%2B+2+\"$
\n" ); document.write( "(3) $\"+q+=+2n+-+3+\"$
\n" ); document.write( "Substitute (2) and (3) into (1)
\n" ); document.write( "(1) $\"+5n+%2B+10%2A%28+3n+%2B+2+%29+%2B+25%2A%28++2n+-+3+%29+=+5725+\"$
\n" ); document.write( "(1) $\"+5n+%2B+30n+%2B+20+%2B+50n+-+75+=+5725+\"$
\n" ); document.write( "(1) $\"+85n+=+5725+%2B+75+-+20+\"$
\n" ); document.write( "(1) $\"+85n+=+5800+-+20+\"$
\n" ); document.write( "(1) $\"+85n+=+5780+\"$
\n" ); document.write( "(1) $\"+n+=+68+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+d+=+3n+%2B+2+\"$
\n" ); document.write( "(2) $\"+d+=+3%2A68+%2B+2+\"$
\n" ); document.write( "(2) $\"+d+=+204+%2B+2+\"$
\n" ); document.write( "(2) $\"+d+=+206+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+q+=+2n+-+3+\"$
\n" ); document.write( "(3) $\"+q+=+2%2A68+-+3+\"$
\n" ); document.write( "(3) $\"+q+=+136+-+3+\"$
\n" ); document.write( "(3) $\"+q+=+133+\"$
\n" ); document.write( "There are 68 nickels, 206 dimes and 133 quarters
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+5%2A68+%2B+10%2A206+%2B+25%2A133+=+5725+\"$
\n" ); document.write( "(1) $\"+340+%2B+2060+%2B+3325+=+5725+\"$
\n" ); document.write( "(1) $\"+5725+=+5725+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );