document.write( "Question 577355: the coins in a piggy bank are all dimes, nickles and quarters. there are twice as many dimes as quarters, and two more nickles than quarters. if the value of all the coins in the bank is $7.60, how many dimes are there? \n" ); document.write( "

Algebra.Com's Answer #370157 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( "given:
\n" ); document.write( "(1) $\"+d+=+2q+\"$
\n" ); document.write( "(2) $\"+n+=+q+%2B+2+\"$
\n" ); document.write( "(3) $\"+5n+%2B+10d+%2B+25q+=+760+\"$ ( in cents )
\n" ); document.write( "-------------------------
\n" ); document.write( "Substitute (10 and (2) into (3)
\n" ); document.write( "(3) $\"+5%2A%28+q+%2B+2+%29+%2B+10%2A%282q%29+%2B+25q+=+760+\"$
\n" ); document.write( "(3) $\"+5q+%2B+10+%2B+20q+%2B+25q+=+760+\"$
\n" ); document.write( "(3) $\"+50q+=+760+-+10+\"$
\n" ); document.write( "(3) $\"+50q+=+750+\"$
\n" ); document.write( "(3) $\"+q+=+15+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+d+=+2q+\"$
\n" ); document.write( "(1) $\"+d+=+2%2A15+\"$
\n" ); document.write( "(1) $\"+d+=+30+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+n+=+q+%2B+2+\"$
\n" ); document.write( "(2) $\"+n+=+15+%2B+2+\"$
\n" ); document.write( "(2) $\"+n+=+17+\"$
\n" ); document.write( "There are 30 dimes
\n" ); document.write( "check:
\n" ); document.write( "(3) $\"+5n+%2B+10d+%2B+25q+=+760+\"$
\n" ); document.write( "(3) $\"+5%2A17+%2B+10%2A30+%2B+25%2A15+=+760+\"$
\n" ); document.write( "(3) $\"+85+%2B+300+%2B+375+=+760+\"$
\n" ); document.write( "(3) $\"+760+=+760+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );