document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=574724>Question 574724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Greeting,<BR>\n" );
document.write( "would you pls help me with this problem (This is the 2nd time that I am submitting this problem without receiving any answer :is it so difficult that no one could even try to solve it?) \r<BR>\n" );
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document.write( "Which equation can be use to solve the following word problem?<BR>\n" );
document.write( "Sam has 6 more nickels than dimes & the total value of his coins is $2.10.<BR>\n" );
document.write( "How many nickels does he have? Let n represent the number of nickels.<BR>\n" );
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document.write( "Thanks a lot<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369258 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=369258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have two unknowns ... the number of nickels and the number of dimes. Call the unknown number of nickels N and call the unknown number of dimes D.<BR>\n" );
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document.write( "Since there are two unknowns, you will need to have two independent equations to solve this problem. So we will need to look for two equations that we can develop from the information that is given in the problem.<BR>\n" );
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document.write( "The first bit of information is that Sam has 6 more nickels that dimes. That means that if we subtract the number of dimes (D) from the number of nickels (N), the answer is 6. So we can write one equation as:<BR>\n" );
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document.write( "N - D = 6 <--- this is our first equation<BR>\n" );
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document.write( "Next you are told that the total value of the coins is $2.10 which is 210 cents. Since each nickel is 5 cents, if we multiply the number of nickels (N) times 5 we will then know the number of cents we have from nickels. Similarly, each dime is 10 cents, so if we multiply the number of dimes (D) times 10 we will then know the number of cents from dimes. And if we then add 5*N and 10*D the total should be 210 cents. In equation form this is:<BR>\n" );
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document.write( "5*N + 10*D = 210  <--- this is our second equation<BR>\n" );
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document.write( "We can solve these two equations by a variable elimination. Let's return to the first equation and get rid of the D on the left side by adding D to both sides as follows:<BR>\n" );
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document.write( "N - D + D = 6 + D<BR>\n" );
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document.write( "On the left side the -D and the +D cancel each other and we are left with:<BR>\n" );
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document.write( "N = 6 + D<BR>\n" );
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document.write( "Now we can go to the second equation and in it replace N with its equal of 6 + D. With this replacement the second equation becomes:<BR>\n" );
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document.write( "5*(6 + D) + 10*D = 210<BR>\n" );
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document.write( "Do the distributed multiplication on the left side by multiplying 5 times both the terms inside the parentheses. When we do that the equation is:<BR>\n" );
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document.write( "30 + 5*D + 10*D = 210<BR>\n" );
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document.write( "Get rid of the 30 on the left side by subtracting 30 from both sides as follows:<BR>\n" );
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document.write( "30 - 30 + 5*D + 10*D = 210 - 30<BR>\n" );
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document.write( "On the left side the 30 - 30 cancel each other and on the right side the subtraction results in 180. So this equation becomes:<BR>\n" );
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document.write( "5*D + 10*D = 180<BR>\n" );
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document.write( "Combine the two terms on the left side and we have:<BR>\n" );
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document.write( "15*D = 180<BR>\n" );
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document.write( "Solve for D by dividing both sides by 15 to get:<BR>\n" );
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document.write( "D = 180/15 = 12<BR>\n" );
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document.write( "So now we know that there are 12 dimes. <BR>\n" );
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document.write( "We can now return to our first equation and replace D with 12 to get:<BR>\n" );
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document.write( "N - 12 = 6<BR>\n" );
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document.write( "Get rid of the 12 on the left side by adding 12 to both sides to get:<BR>\n" );
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document.write( "N - 12 + 12 = 6 + 12<BR>\n" );
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document.write( "The left side reduces to just N and the right side totals 18, making the equation:<BR>\n" );
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document.write( "N = 18<BR>\n" );
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document.write( "So we now know that there are 18 nickels and 12 dimes.<BR>\n" );
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document.write( "We can see that there are 6 more nickels than dimes. That checks with what the problem says. And we can figure out the total value of the money. Since there are 5 cents for every nickel, we can multiply 5 times the 18 nickels and see that we have 90 cents worth of nickels. And since there are 10 cents for each dime and we have 12 dimes, we multiply 10 times 12 and see that there are 120 cents worth of cents in our 12 dimes. Adding together the 90 cents worth of nickels and 120 cents worth of dimes, we get a total value of 210 cents or $2.10, just as the problem says it should be. So our answer checks out entirely. <BR>\n" );
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document.write( "And we can answer the problem by stating that there are 18 nickels.<BR>\n" );
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document.write( "Hope that this helps you to understand this problem and how to go about solving it.<BR>\n" );
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