document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097683>Question 1097683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a purse Misty has 1.91, including one more nickel than quarters. She also has twice as many dimes as nickels. But, she also has eight more pennies than dimes. How many of each of the four coins does Misty have?\r<BR>\n" );
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document.write( "So what I did was use the formula: Quantity X Value = Subtotal. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712162 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=712162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Solving problems like this with formal algebra is of course good exercise in learning algebra.  However, thinking through a problem with logical analysis can be an even better exercise for your brain.  So let's think through this problem using the clues we have to find the answer.  Then we can look at a formal algebraic solution.<br><BR>\n" );
document.write( "The total value is $1.91, made up of pennies, nickels, dimes, and quarters.  Since pennies are the only coins with values that are not multiples of 5, the number of pennies has to be one of these:<BR>\n" );
document.write( "  1, 6, 11, 16, 21, 26, ... etc.<br><BR>\n" );
document.write( "But the number of pennies is 8 more than the number of dimes, so the number of pennies can't be 1 or 6.<br><BR>\n" );
document.write( "So let's guess that the number of pennies is 11, and see what happens.<br><BR>\n" );
document.write( "The number of pennies is 11, so the number of dimes is 3.  The number of dimes is twice the number of nickels,....<br><BR>\n" );
document.write( "Oops! This isn't going to work; the number of dimes has to be an even number.<br><BR>\n" );
document.write( "So next let's see what happens if we guess the number of pennies is 16.<br><BR>\n" );
document.write( "The number of pennies is 16, so the number of dimes is 8; then the number of nickels is 4.  And using some information we haven't yet had a chance to use, the number of quarters is then 3.<br><BR>\n" );
document.write( "So we have a potential answer of 3 quarters, 8 dimes, 4 nickels, and 16 pennies.<br><BR>\n" );
document.write( "Does that give us the right total?  Let's check.<br><BR>\n" );
document.write( "3(25) + 8(10) + 4(5) + 16(1) = 75+80+20+16 = 191<br><BR>\n" );
document.write( "Hooray!  We found the answer.<br><br><BR>\n" );
document.write( "Now for a solution using formal algebra.<br><BR>\n" );
document.write( "You want to look for a way to define your variable(s) so that the work you have to do is as easy as possible.  In particular, it is generally a good idea to avoid fractions if possible.  In this problem, a bit of analysis shows that using either the number of quarters or the number of nickels is best.  Then since the number of nickels is 1 more than the number of quarters, let's choose the number of quarters for our variable.<br><BR>\n" );
document.write( "let x = number of quarters<BR>\n" );
document.write( "then x+1 = number of nickels  [one more than the number of quarters]<BR>\n" );
document.write( "then 2x+2 = number of dimes  [twice the number of nickels]<BR>\n" );
document.write( "then 2x+10 = number of pennies  [8 more than the number of dimes]<br><BR>\n" );
document.write( "Now use your formula with these expressions and the values of each coin:<br><BR>\n" );
document.write( "value of the quarters: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28x%29+=+25x ALIGN=MIDDLE  ALT=\"25%28x%29+=+25x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "value of the nickels: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%2B1%29+=+5x%2B5 ALIGN=MIDDLE  ALT=\"5%28x%2B1%29+=+5x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "value of the dimes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%282x%2B2%29+=+20x%2B20 ALIGN=MIDDLE  ALT=\"10%282x%2B2%29+=+20x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "value of the pennies: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%282x%2B10%29+=+2x%2B10 ALIGN=MIDDLE  ALT=\"1%282x%2B10%29+=+2x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the total value of all the coins is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825x%29%2B%285x%2B5%29%2B%2820x%2B20%29%2B%282x%2B10%29+=+191 ALIGN=MIDDLE  ALT=\"%2825x%29%2B%285x%2B5%29%2B%2820x%2B20%29%2B%282x%2B10%29+=+191\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52x%2B35+=+191 ALIGN=MIDDLE  ALT=\"52x%2B35+=+191\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52x+=+156 ALIGN=MIDDLE  ALT=\"52x+=+156\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now go back and substitute this value into the expressions for the numbers of the different coins; you get the answer:<BR>\n" );
document.write( "3 quarters, 4 nickels, 8 dimes, 16 pennies </SPAN>\n" );
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