document.write( "Question 232942: A collection of coins consisting of dimes and quarters amounts to $5.35. Twice the number of dimes exceeds the number of quarters by 5. Find the number of each kind of coin. \n" ); document.write( "

Algebra.Com's Answer #172030 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"d\"$ = number of dimes
\n" ); document.write( "Let $\"q\"$ = number of quarters
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"10d+%2B+25q+=+535\"$ (in cents)
\n" ); document.write( "(2) $\"2d+=+q+%2B+5\"$
\n" ); document.write( "----------------
\n" ); document.write( "This is 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "Subtract $\"q\"$ from both sides of (2)
\n" ); document.write( "(2) $\"2d+-+q+=+5\"$
\n" ); document.write( "Now multiply both sides by $\"5\"$
\n" ); document.write( "and subtract (2) from (1)
\n" ); document.write( "(1) $\"10d+%2B+25q+=+535\"$
\n" ); document.write( "(2) $\"-10d+%2B+5q+=+-25\"$
\n" ); document.write( " $\"30q+=+510\"$
\n" ); document.write( " $\"q+=+17\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"2d+=+q+%2B+5\"$
\n" ); document.write( " $\"2d+=+17+%2B+5\"$
\n" ); document.write( " $\"2d+=+22\"$
\n" ); document.write( " $\"d+=+11\"$
\n" ); document.write( "There are 17 quarters and 11 dimes
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"10d+%2B+25q+=+535\"$
\n" ); document.write( " $\"10%2A11+%2B+25%2A17+=+535\"$
\n" ); document.write( " $\"110+%2B+425+=+535\"$
\n" ); document.write( " $\"535+=+535\"$
\n" ); document.write( "OK \n" ); document.write( "

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