document.write( "Question 120443: mr m has 3 times as many quarters as dimes, if he has a total of $6.80 in quarters and dimes, how many of each does he have. \r
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Algebra.Com's Answer #88279 by bucky(2189)\"\" \"About 
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Let D be the number of dimes and Q be the number of quarters.
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\n" ); document.write( "Since there are 3 times as many quarters as dimes, if you multiply the number of dimes by 3
\n" ); document.write( "the answer will be the same as the number of quarters. In equation form this becomes:
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\n" ); document.write( "3D = Q
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\n" ); document.write( "Each dime is 0.1 of a dollar. So if you multiply the number of dimes D by 0.1 you get the
\n" ); document.write( "amount in dollars that come from dimes. The resulting term is 0.1D.
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\n" ); document.write( "Each quarter is 0.25 of a dollar. So if you multiply the number of quarters Q by 0.25 you get
\n" ); document.write( "the amount in dollars that come from quarters. The resulting term is 0.25Q.
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\n" ); document.write( "The problem tells you that adding these two terms will result in $6.80. In equation
\n" ); document.write( "form this is:
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\n" ); document.write( "0.1D + 0.25Q = 6.80
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\n" ); document.write( "From our first equation we know that Q = 3D. This tells us that we can go to our dollar equation
\n" ); document.write( "and substitute 3D for Q. This substitution leads to:
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\n" ); document.write( "0.1D + 0.25(3D) = 6.80
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\n" ); document.write( "Multiply out the second term on the left side and you get:
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\n" ); document.write( "0.1D + 0.75D = 6.80
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\n" ); document.write( "Add the two terms on the left side to get:
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\n" ); document.write( "0.85D = 6.80
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\n" ); document.write( "Solve for D by dividing both sides of this equation by 0.85:
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\n" ); document.write( "D = 6.80/0.85 = 8
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\n" ); document.write( "This tells you that the number of dimes equals 8
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\n" ); document.write( "Since the number of quarters is three times the number of dimes, then the number of quarters
\n" ); document.write( "is 8*3 = 24.
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\n" ); document.write( "Let's check ... each 4 quarters is a dollar ... and there are six groups of 4 quarters, then
\n" ); document.write( "the number of dollars from quarters is $6.00
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\n" ); document.write( "and the 8 dimes is 80 cents or $0.80.
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\n" ); document.write( "The sum of these two amounts is $6.00 + $0.80 = $6.80, just as the problem said it should.
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\n" ); document.write( "And with 24 quarters and 8 dimes, there are 3 times as many quarters as there are dimes.
\n" ); document.write( "This is also as the problem said it should be. Therefore, the answer of 24 quarters and
\n" ); document.write( "8 dimes fully checks out.
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\n" ); document.write( "Hope this helps you to understand the problem and how to solve it algebraically.
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