document.write( "Question 219001: Tim had $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer. He has five more nickels than quarters, the number of pennies is two-thirds the number of nickles, there are half as many dimes as nickels.How many coins of each type does he have? \n" ); document.write( "

Algebra.Com's Answer #164818 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"q\"$ = number of quarters he has
\n" ); document.write( "Let $\"d\"$ = number of dimes he has
\n" ); document.write( "Let $\"n\"$ = number of nickels he has
\n" ); document.write( "Let $\"p\"$ = number of pennies he has
\n" ); document.write( "Let $\"h\"$ = number of half-dollars he has\r
\n" ); document.write( "\n" ); document.write( "Just by looking at the amount of money Tim has,
\n" ); document.write( "you can tell a lot about the coins that make it up.
\n" ); document.write( "(1) The number of half dollars must be less than
\n" ); document.write( " $\"10\"$ , since that would leave no room for other coins
\n" ); document.write( "(2) He must have at least 3 pennies to get $5.53.
\n" ); document.write( "-----------------------------------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"n+=+q+%2B+5\"$
\n" ); document.write( "(2) $\"p+=+%282%2F3%29%2An\"$
\n" ); document.write( "(3) $\"d+=+n%2F2\"$
\n" ); document.write( "(4) $\"10d+%2B+5n+%2B+p+%2B+25q+%2B+50h+=+503\"$ (in pennies)
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "There are $\"5\"$ unknowns and only $\"4\"$ equations, so
\n" ); document.write( "it will take some extra work to get the answer
\n" ); document.write( "From (1), $\"q+=+n+-+5\"$
\n" ); document.write( "Substituting into (4),
\n" ); document.write( " $\"10%2A%28n%2F2%29+%2B+5n+%2B+%282%2F3%29%2An+%2B+25%2A%28n-5%29+%2B+50h+=+503\"$
\n" ); document.write( "Multiply both sides by $\"6\"$
\n" ); document.write( " $\"30n+%2B+30n+%2B+4n+%2B+150%2A%28n-5%29+%2B+300h+=+3018\"$
\n" ); document.write( " $\"64n+%2B+150n+-+750+%2B+300h+=+3018\"$
\n" ); document.write( " $\"214n+%2B+300h+=+3768\"$
\n" ); document.write( " $\"107n+%2B+150h+=+1884\"$
\n" ); document.write( "I need a combination of $\"n\"$ and $\"h\"$ that
\n" ); document.write( "will give me $\"1884\"$ , and $\"h\"$ must be $\"9\"$ or less
\n" ); document.write( "--------------------
\n" ); document.write( " $\"107%2A1+%2B+150%2A9+=+1457\"$
\n" ); document.write( " $\"107%2A2+%2B+150%2A9+=+1564\"$
\n" ); document.write( " $\"107%2A3+%2B+150%2A9+=+1671\"$
\n" ); document.write( " $\"107%2A4+%2B+150%2A9+=+1778\"$
\n" ); document.write( " $\"107%2A5+%2B+150%2A9+=+1885\"$
\n" ); document.write( "There can't be $\"9\"$ half-dollars,
\n" ); document.write( "I'll try $\"8\"$ halfs
\n" ); document.write( " $\"107%2A5+%2B+150%2A8+=+1735\"$
\n" ); document.write( " $\"107%2A6+%2B+150%2A8+=+1842\"$
\n" ); document.write( "Can't be it, increasing $\"n\"$ takes me over $\"1884\"$
\n" ); document.write( " $\"107%2A6+%2B+150%2A7+=+1592\"$
\n" ); document.write( " $\"107%2A7+%2B+150%2A7+=+1799\"$
\n" ); document.write( "Next increase in $\"n\"$ takes me over $\"1884\"$
\n" ); document.write( " $\"107%2A8+%2B+150%2A6+=+1756\"$
\n" ); document.write( " $\"107%2A9+%2B+150%2A6+=+1863\"$
\n" ); document.write( "not it
\n" ); document.write( " $\"107%2A10+%2B+150%2A5+=+1820\"$
\n" ); document.write( " $\"107%2A12+%2B+150%2A5+=+2034\"$
\n" ); document.write( "not it
\n" ); document.write( " $\"107%2A12+%2B+150%2A4+=+1884\"$ BINGO
\n" ); document.write( "Now I know that
\n" ); document.write( " $\"n+=+12\"$
\n" ); document.write( " $\"h+=+4\"$
\n" ); document.write( "and
\n" ); document.write( " $\"p+=+%282%2F3%29%2An\"$
\n" ); document.write( " $\"p+=+%282%2F3%29%2A12\"$
\n" ); document.write( " $\"p+=+8\"$
\n" ); document.write( "and
\n" ); document.write( " $\"q+=+n+-+5\"$
\n" ); document.write( " $\"q+=+12+-+5\"$
\n" ); document.write( " $\"q+=+7\"$
\n" ); document.write( "and
\n" ); document.write( " $\"d+=+n%2F2\"$
\n" ); document.write( " $\"d+=+6\"$
\n" ); document.write( "Tim has 8 pennies, 12 nickels, 6 dimes, 7 quarters, and 4 half-dollars
\n" ); document.write( "check answer:
\n" ); document.write( "(4) $\"10d+%2B+5n+%2B+p+%2B+25q+%2B+50h+=+503\"$
\n" ); document.write( " $\"10%2A6+%2B+5%2A12+%2B+1%2A8+%2B+25%2A7+%2B+50%2A4+=+503\"$
\n" ); document.write( " $\"60+%2B+60+%2B+8+%2B+175+%2B+200+=+503\"$
\n" ); document.write( " $\"503+=+503\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );