document.write( "Question 241985: bill has 10 coins which are quarters and dimes if his quarters were dimes and his dimes were quarters the total is 30 cents more how many quarters does he has? \n" ); document.write( "

Algebra.Com's Answer #177167 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"d\"$ = number of dimes he has
\n" ); document.write( "Let $\"q\"$ = number of quarters he has
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"d+%2B+q+=+10\"$
\n" ); document.write( "(2) $\"10d+%2B+25q+%2B+30+=+10q+%2B+25d\"$
\n" ); document.write( "---------------------------------------
\n" ); document.write( "Notice that on the right side, I make the quarters
\n" ); document.write( "worth $\"10\"$ each and dimes worth $\"25\"$ each
\n" ); document.write( "From (1):
\n" ); document.write( "(1) $\"q+=+10+-+d\"$
\n" ); document.write( "And, substituting:
\n" ); document.write( "(2) $\"10d+%2B+25%2A%2810+-+d%29+%2B+30+=+10%2A%2810+-+d%29+%2B+25d\"$
\n" ); document.write( " $\"10d+%2B+250+-+25d+%2B+30+=+100+-+10d+%2B+25d\"$
\n" ); document.write( " $\"-15d+%2B+280+=+15d+%2B+100\"$
\n" ); document.write( " $\"30d+=+180\"$
\n" ); document.write( " $\"d+=+6\"$
\n" ); document.write( "And, since
\n" ); document.write( " $\"q+=+10+-+d\"$
\n" ); document.write( " $\"q+=+4\"$
\n" ); document.write( "He has 4 quarters
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"10d+%2B+25q+%2B+30+=+10q+%2B+25d\"$
\n" ); document.write( " $\"10%2A6+%2B+25%2A4+%2B+30+=+10%2A4+%2B+25%2A6\"$
\n" ); document.write( " $\"60+%2B+100+%2B+30+=+40+%2B+150\"$
\n" ); document.write( " $\"190+=+190\"$
\n" ); document.write( "OK \r
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