document.write( "Question 216017: If there are 500 coins in total (consisting of half-dollars, dimes and pennies), and it totals $25.00, what is the combination of coins? How many half-dollars, dimes and pennies? Show the algebra. \n" ); document.write( "
Algebra.Com's Answer #163185 by ankor@dixie-net.com(22740)\"\" \"About 
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If there are 500 coins in total (consisting of half-dollars, dimes and pennies),
\n" ); document.write( " and it totals $25.00, what is the combination of coins?
\n" ); document.write( " How many half-dollars, dimes and pennies? Show the algebra.
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\n" ); document.write( "Let h = no. of half dollars
\n" ); document.write( "Let d = no. of dimes
\n" ); document.write( "Let p = pennies
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\n" ); document.write( "\"If there are 500 coins in total\"
\n" ); document.write( "h + d + p = 500
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\n" ); document.write( "\"it totals $25.00,\"
\n" ); document.write( ".50h + .10d + .01p = 25
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\n" ); document.write( "what is the combination of coins? How many half-dollars, dimes and pennies?
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\n" ); document.write( "eliminate p and see what we can come up with, multiply the $$ equation by 100
\n" ); document.write( "Subtract the total coin equaion (makes .01p = p)
\n" ); document.write( "50h + 10d + p = 2500
\n" ); document.write( " h + d + p = 500
\n" ); document.write( "---------------------subtraction eliminates p
\n" ); document.write( "49h + 9d = 2000
\n" ); document.write( "9d = 2000 - 49h
\n" ); document.write( "d = \"%282000-49h%29%2F9\"
\n" ); document.write( "d has to be an integer and the number of half-dollars is low,
\n" ); document.write( " substitute values for h which will yield an integer value for d
\n" ); document.write( "Try h = 5
\n" ); document.write( "d = \"%282000-49%285%29%29%2F9\"
\n" ); document.write( "d = \"%282000-245%29%2F9\"
\n" ); document.write( "d = \"%281755%29%2F9\"
\n" ); document.write( "d = 195 dimes and 5 half dollars
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\n" ); document.write( "Then: 500 - 195 - 5 = 300 pennies
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\n" ); document.write( " 5 half-dollars, 195 dimes, and 300 pennies
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\n" ); document.write( "Check solution by finding the value
\n" ); document.write( ".5(5) + .10(195) + .01(300) =
\n" ); document.write( "2.50 + 19.50 + 3.00 = 25.00
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\n" ); document.write( "An interesting note
\n" ); document.write( "I put this equation into the Ti83 and found there are 3 other solutions
\n" ); document.write( "for example:
\n" ); document.write( " 14 half-dollars, 146 dimes and 340 pennies
\n" ); document.write( " 23 half-dollars, 97 dimes and 380 pennies
\n" ); document.write( " 32 half-dollars, 48 dimes and 420 pennies
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