document.write( "Question 743784: Michael's bank contains only nickels, dimes, and quarters. There are 50 coins is all, value at $4.15. The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank? \n" ); document.write( "

Algebra.Com's Answer #852668 by ikleyn(53266) $\"\"$ $\"About$

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\n" ); document.write( "Michael's bank contains only nickels, dimes, and quarters. There are 50 coins is all, value at $4.15.
\n" ); document.write( "The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together.
\n" ); document.write( "How many dimes are in the bank?
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document.write( "Let' solve it mentally.\r\n" );
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document.write( "Let's add 10 short nickels mentally. We will get 50+10 = 60 coins, with the number of nickels being three times \r\n" );
document.write( "of the sum of the number of dimes and quarters together.\r\n" );
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document.write( "It means that four times the number of dimes and quarters is 60/4 = 15 in the original collection,\r\n" );
document.write( "with the number of nickels 3*15 - 10 = 35 in the original collection.\r\n" );
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document.write( "So, the original collection is 35 nickels plus 15 dimes and quarters (dimes and quarters are counted together).\r\n" );
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document.write( "Hence, 15 dimes and quarters in the original collection are worth 415 - 35*5 = 240 cents.\r\n" );
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document.write( "Had all 15 coins be dimes, it would be 150 cents, but we actually have 240 cents, or 90 cents more.\r\n" );
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document.write( "Hence, some dimes should be replaced by quarters.\r\n" );
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document.write( "Each such replacement increases the value of dimes and quarters by 15 cents, and the number of such replacements\r\n" );
document.write( "should be, therefore, 90/15 = 6.\r\n" );
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document.write( "Thus, the original collection has 35 nickels, 6 quarters and 50 - 35 - 6 = 9 dimes.\r\n" );
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document.write( "CHECK.  Total coins = 35 + 6 + 9 = 50.\r\n" );
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document.write( "        Total money = 35*5 + 6*25 + 9*10 = 415 cents, or $4.15.\r\n" );
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document.write( "        The number of nickels is 3*(6+9) -10 = 3*15 - 10 = 45 - 10 = 35.\r\n" );
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document.write( "        Everything is correct.\r\n" );
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document.write( "ANSWER.  35 nickels, 9 dimes and 6 quarters.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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