document.write( "Question 461117: Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. How many coins of each kind does she have? \n" ); document.write( "

Algebra.Com's Answer #316266 by stanbon(75887) $\"\"$ $\"About$

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Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. How many coins of each kind does she have?
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\n" ); document.write( "Quantity Equation: n + d + q = 105 coins
\n" ); document.write( "Quantity Equation: d = (1/3)n + 5
\n" ); document.write( "Quantity Equation: q = 2d
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\n" ); document.write( "Substitute for d and q and solve for \"n\":
\n" ); document.write( "n + (1/3)n + 5 + 2d = 105
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\n" ); document.write( "(4/3)n + 5 + (2/3)n + 10 = 105
\n" ); document.write( "2n + 15 = 105
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\n" ); document.write( "2n = 90
\n" ); document.write( "n = 45 (number of nickels)
\n" ); document.write( "d = (1/3)n+5 = 15+5 = 20 (number of dimes)
\n" ); document.write( "q = 2d = 40 (number of quarters)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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