document.write( "Question 187158: Pocket change: Harry has $2.25 in nickels, dimes, and quarters. If he had twice as many nickels, half as many dimes and the same number of quarters, he would have $2.50. If he has 27 coins altogether, then how many of each does he have?\r
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\n" ); document.write( "\n" ); document.write( "2) Three digit number: The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than 5 times the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number? \n" ); document.write( "

Algebra.Com's Answer #140288 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) $\"5n+%2B+10d+%2B+25q+=+225\"$
\n" ); document.write( "(2) $\"5%2A2n+%2B+10%2A%281%2F2%29%2Ad+%2B+25q+=+250\"$
\n" ); document.write( "(3) $\"n+%2B+d+%2B+q+=+27\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "There are 3 unknowns and 3 equations, so it's solvable
\n" ); document.write( "(2) $\"5%2A2n+%2B+10%2A%281%2F2%29%2Ad+%2B+25q+=+250\"$
\n" ); document.write( "(2) $\"10n+%2B+5d+%2B+25q+=+250\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"10n+%2B+5d+%2B+25q+=+250\"$
\n" ); document.write( "(1) $\"-5n+-+10d+-+25q+=+-225\"$
\n" ); document.write( "(4) $\"5n+-+5d+=+25\"$
\n" ); document.write( "(4) $\"n+-+d+=+5\"$
\n" ); document.write( "(4) $\"d+=+n+-+5\"$
\n" ); document.write( "And, from (3),
\n" ); document.write( "(3) $\"n+%2B+d+%2B+q+=+27\"$
\n" ); document.write( "(3) $\"q+=+-n+-+d+%2B+27\"$
\n" ); document.write( "From(1)
\n" ); document.write( "(1) $\"5n+%2B+10d+%2B+25q+=+225\"$
\n" ); document.write( "(1) $\"n+%2B+2d+%2B+5q+=+45\"$
\n" ); document.write( "(1) $\"n+%2B+2%2A%28n+-+5%29+%2B+5%2A%28-n+-d+%2B+27%29+=+45\"$
\n" ); document.write( "(1) $\"n+%2B+2n+-+10+-+5n+-+5d+%2B+135+=+45\"$
\n" ); document.write( "(1) $\"-2n+-+5d+=+-80\"$
\n" ); document.write( "(1) $\"-2n+-+5%2A%28n+-+5%29+=+-80\"$
\n" ); document.write( "(1) $\"-2n+-5n+%2B+25+=+-80\"$
\n" ); document.write( "(1) $\"-7n+=+-105\"$
\n" ); document.write( "(1) $\"+n+=+15\"$
\n" ); document.write( "and
\n" ); document.write( "(4) $\"d+=+n+-+5\"$
\n" ); document.write( "(4) $\"d+=+10\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"q+=+-n+-+d+%2B+27\"$
\n" ); document.write( "(3) $\"q+=+-15+-+10+%2B+27\"$
\n" ); document.write( "(3) $\"q+=+-25+%2B+27\"$
\n" ); document.write( "(3) $\"q+=+2\"$
\n" ); document.write( "Harry has 15 nickels, 10 dimes, and 2 quarters
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"5n+%2B+10d+%2B+25q+=+225\"$
\n" ); document.write( "(1) $\"5%2A15+%2B+10%2A10+%2B+25%2A2+=+225\"$
\n" ); document.write( "(1) $\"75+%2B+100+%2B+50+=+225\"$
\n" ); document.write( "(1) $\"225+=+225\"$
\n" ); document.write( "OK \n" ); document.write( "

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