document.write( "Question 536473: Katie has 30 coins. Some are dimes and some are nickels. In all she has $2.10. How many nickels and dimes does she have? \n" ); document.write( "

Algebra.Com's Answer #352381 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"d\"$ = number of dimes
\n" ); document.write( "Let $\"n\"$ = number of nickels
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+d+%2B+n+=+30+\"$
\n" ); document.write( "(2) $\"+10d+%2B+5n+=+210+\"$ ( in cents )
\n" ); document.write( "-----------------
\n" ); document.write( "Multiply both sides of (1) by $\"5\"$
\n" ); document.write( "then subtract (1) from (2)
\n" ); document.write( "(2) $\"+10d+%2B+5n+=+210+\"$
\n" ); document.write( "(1) $\"+-5d+-+5n+=+-150+\"$
\n" ); document.write( " $\"+5d+=+60+\"$
\n" ); document.write( " $\"+d+=+12+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+d+%2B+n+=+30+\"$
\n" ); document.write( "(1) $\"+12+%2B+n+=+30+\"$
\n" ); document.write( "(1) $\"+n+=+30+-+12+\"$
\n" ); document.write( "(1) $\"+n+=+18+\"$
\n" ); document.write( "She has 12 dimes and 18 nickels
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+10%2A12+%2B+5%2A18+=+210+\"$
\n" ); document.write( "(2) $\"+120+%2B+90+=+210+\"$
\n" ); document.write( "(2) $\"+210+=+210+\"$
\n" ); document.write( "OK \n" ); document.write( "

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