document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204021>Question 204021</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have tried...for several hours. :( I absolutely can not translate this word problem and solve it correctly. I truly appreciate any help with this.<BR>\n" );
document.write( "PROBLEM:<BR>\n" );
document.write( "A storekeeper goes to the bank to get $10 worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickles as dimes and no pennies or dollars. How many of each coin did the storekeeper get? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153939 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=153939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, the first step is to assign variables to each of the unknowns in the problem:<BR>\n" );
document.write( "Let:<BR>\n" );
document.write( "H = # of half-dollars.<BR>\n" );
document.write( "Q = # of quarters.<BR>\n" );
document.write( "D = # of dimes.<BR>\n" );
document.write( "N = # of nickels.<BR>\n" );
document.write( "Now to translate the English prose to algebraic statements:<BR>\n" );
document.write( "Q = 2H \"...twice as many quarters as half-dollars,...\"<BR>\n" );
document.write( "D = 2Q \"...twice as many dimes as quarters,...\"<BR>\n" );
document.write( "N = 3D \"...three times as many nickels as dimes...\"<BR>\n" );
document.write( "Now we can write an equation relating all four varables (H, Q, D, and N) to the total amount tendered at the bank ($10.00)<BR>\n" );
document.write( "For example, the dollar-value of H half dollars can be expressed as: (0.5)H, so...<BR>\n" );
document.write( "(0.5)H+(0.25)Q+(0.1)D+(0.05)N = $10.00<BR>\n" );
document.write( "Now the trick is to reduce the number of variables from four down to one! It really doesn't matter which variable you choose but try to pick the easiest path to getting it.<BR>\n" );
document.write( "I picked the variable H, the number of half-dollars.<BR>\n" );
document.write( "Here we go!<BR>\n" );
document.write( "N = 3D substitute D = 2Q to get:<BR>\n" );
document.write( "N = 3(2Q) = 6Q substitute Q = 2H<BR>\n" );
document.write( "N = 3(2(2H)) or (3(4H)) so...<BR>\n" );
document.write( "N = 12H<BR>\n" );
document.write( "D = 2Q substitute Q = 2H, so...<BR>\n" );
document.write( "D = 2(2H) = 4H<BR>\n" );
document.write( "So now we have:<BR>\n" );
document.write( "Q = 2H<BR>\n" );
document.write( "D = 4H<BR>\n" );
document.write( "N = 12H so we can substitute into the first equation to get:<BR>\n" );
document.write( "(0.5)H+(0.25)(2H)+(0.1)(4H)+(0.05)(12H) = 10 Add the H's together:<BR>\n" );
document.write( "(0.5)H+(0.5)H+0.4H+0.6H = 10<BR>\n" );
document.write( "2H = 10 Divide both sides by 2.<BR>\n" );
document.write( "H = 5 and...<BR>\n" );
document.write( "Q = 2H = 10 and...<BR>\n" );
document.write( "D = 4H = 20 and...<BR>\n" );
document.write( "N = 12H = 60, so...<BR>\n" );
document.write( "The store-keeper got:<BR>\n" );
document.write( "5 Half-dollars.<BR>\n" );
document.write( "10 Quarters.<BR>\n" );
document.write( "20 Dimes.<BR>\n" );
document.write( "60 Nickels.<BR>\n" );
document.write( "Now let's check to see if this all adds up tp $10.00<BR>\n" );
document.write( "(0.5)5+(0.25)(10)+(0.1)(20)+(0.05)(60) = 2.5+2.5+2+3 = 10 OK!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );