document.write( "Question 1034271: A collection of nickels, dimes, and quarters consist of 60 coins with a total of $6.50. If there are 3 times as many dimes as quarters, find the number of each type of coins. \n" ); document.write( "

Algebra.Com's Answer #648879 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A collection of nickels, dimes, and quarters consist of 60 coins with a total of $6.50.
\n" ); document.write( "If there are 3 times as many dimes as quarters, find the number of each type of coins.
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document.write( "From the condition, you have these tree equations for three unknowns\r\n" );
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document.write( "n + d + q = 60,              (1)\r\n" );
document.write( "d = 3q,                      (2)\r\n" );
document.write( "5n + 10d + 25q = 650.        (3)\r\n" );
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document.write( "Since you have 3 independent equations for three unknowns, it is enough to get the solution.\r\n" );
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document.write( "Substitute d = 3q from the equation (2) first into equation (1) and then into equation (3).\r\n" );
document.write( "In this way you exclude the unknown d and will get the system of TWO equations in TWO unknowns\r\n" );
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document.write( "n + 3q + q = 60,             (1')\r\n" );
document.write( "5n + 10*(3q) + 25q = 650.    (2')\r\n" );
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document.write( "or simplifying,\r\n" );
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document.write( " n +  4q =  60,              (1'')\r\n" );
document.write( "5n + 55q = 650.              (2'')\r\n" );
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document.write( "To solve this system, let's do one more step of the substitution method.\r\n" );
document.write( "Express n = 60 - 4q from (1'') and substitute it into equation (2''). You will get\r\n" );
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document.write( "5*(60-4q) + 55q = 650.\r\n" );
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document.write( "Simplify and solve it for q:\r\n" );
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document.write( "300 - 20q + 55q = 650,\r\n" );
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document.write( "35q = 650 - 300,\r\n" );
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document.write( "35q = 350,\r\n" );
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document.write( "q = 10.\r\n" );
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document.write( "Congratulations! You just found the number of quarters.\r\n" );
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document.write( "Now you can find the number of nickels. \r\n" );
document.write( "Use the formula n = 60 - 4q that you obtained above. You will get\r\n" );
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document.write( "n = 60 - 4*10 = 60 - 40 = 20.   So, the number of nickels is 20.\r\n" );
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document.write( "Last step is to find the number of dimes. For it, use the formula d= 3q (equation (2)). You have d = 3*10 = 30.\r\n" );
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document.write( "Answer. n = 20, d = 30, q = 10.\r\n" );
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document.write( "Please check yourself that the solution is correct.\r\n" );
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