document.write( "Question 155215: You have a total of $4564.50 in coins. There are 8 times as many half-dollars as quarters and 6 times as many dimes as nickels. How many coins were there of each kind \n" ); document.write( "
Algebra.Com's Answer #114318 by ankor@dixie-net.com(22740)\"\" \"About 
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You have a total of $4564.50 in coins. There are 8 times as many half-dollars as quarters and 6 times as many dimes as nickels. How many coins were there of each kind?
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\n" ); document.write( "We have 4 unknowns and only 3 equations here. There is more than one solution.
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\n" ); document.write( "Simplify as much as we can:
\n" ); document.write( ".05n + .10d + .25q + .50h = 4564.50
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\n" ); document.write( "It says: h = 8q, and d = 6n, substitute for h and d in the above equation:
\n" ); document.write( ":
\n" ); document.write( ".05n + .10(6n) + .25q + .50(8q) = 4564.50
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\n" ); document.write( ".05n + .60n + .25q + 4q = 4564.50
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\n" ); document.write( ".65n + 4.25q = 4564.50
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\n" ); document.write( "Using a calc, I found a value for q that gives an integer value for n:
\n" ); document.write( "Let q = 450 quarters.
\n" ); document.write( "then
\n" ); document.write( ".65n + 4.25(450) = 4564.50
\n" ); document.write( ".65n + 1912.50 = 4564.50
\n" ); document.write( ".65n = 4564.50 - 1912.50
\n" ); document.write( ".65n = 2652
\n" ); document.write( "n = \"2652%2F.65\"
\n" ); document.write( "n = 4080 nickels
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\n" ); document.write( "Find the no. of dimes:
\n" ); document.write( "d = 6*4080
\n" ); document.write( "d = 24480 dimes
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\n" ); document.write( "Find no. of half dollars
\n" ); document.write( "h = 8*450
\n" ); document.write( "h = 3600 half dollars
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\n" ); document.write( "Check solutions total:
\n" ); document.write( ".05(4080) + .10(24480) + .25(450) + .5(3600) =
\n" ); document.write( " 204 + 2448 + 112.50 + 1800 = 4564.50
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\n" ); document.write( "However, there are many other solutions, you can check using other values for q:
\n" ); document.write( "q = 34, 47, 60, 73, 86, 99, 112, 125; you can see starting at 34, every 13th no.
\n" ); document.write( "will give an integer value for n. \n" ); document.write( "
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