document.write( "Question 961723: A vending machine has $6.30 in it. There are 52 coins total and the machine only accepts nickels, dimes, and quarters. There are five more dimes than nickels. How many of each coin are in the machine. \n" ); document.write( "

Algebra.Com's Answer #808168 by CubeyThePenguin(3113) $\"\"$ $\"About$

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n = number of nickels
\n" ); document.write( "d = number of dimes
\n" ); document.write( "q = number of quarters\r
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\n" ); document.write( "\n" ); document.write( "n + d + q = 52
\n" ); document.write( "d = n + 5
\n" ); document.write( "5n + 10d + 25q = 630\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(substituting d = n + 5 into the first and third equations)
\n" ); document.write( "2n + q = 47
\n" ); document.write( "15n + 25q = 580\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Multiply the first equation by 25 (eliminating q)
\n" ); document.write( "50n + 25q = 1175
\n" ); document.write( "-15n - 25q = -580
\n" ); document.write( "---------------------
\n" ); document.write( "35n = 595
\n" ); document.write( "n = 17
\n" ); document.write( "d = 17 + 5 = 22
\n" ); document.write( "q = 52 - 17 - 22 = 13\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---> There are 17 nickels, 22 dimes, and 13 quarters. \n" ); document.write( "

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