document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123892>Question 123892</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mrs Lee bought 40 fun fair coupons. Some of the coupons were worth $2 and the rest were worth $5. The total value of all the coupons was $146. How many $5 coupons did Mrs Lee buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90893 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=90893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let T represent the number of $2 coupons and F represent the number of $5 coupons.<BR>\n" );
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document.write( "The problem tells you that a total of 40 coupons were purchased. Therefore, we can write an equation<BR>\n" );
document.write( "about the total number of coupons. The numbers of each type of coupon must total 40. In equation<BR>\n" );
document.write( "form this is:<BR>\n" );
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document.write( "T + F = 40<BR>\n" );
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document.write( "The number of dollars spent on $2 coupons is the $2 multiplied by the number of $2 coupons purchased.<BR>\n" );
document.write( "Since the number of $2 coupons purchased is the unknown T, the total dollar value of the $2<BR>\n" );
document.write( "coupons is $2 times T or simply 2T. Similarly, the amount spent of $5 coupons is $5 times the<BR>\n" );
document.write( "number of $5 coupons purchased or $5 times F or simply 5F. The total spent is $146, so we can<BR>\n" );
document.write( "write the equation totaling the amounts spent for each type of coupon as:<BR>\n" );
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document.write( "2T + 5F = 146<BR>\n" );
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document.write( "Returning to the first equation for the total number of coupons sold we can subtract <BR>\n" );
document.write( "F from both sides of the equation to find that:<BR>\n" );
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document.write( "T = 40 - F<BR>\n" );
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document.write( "So we can substitute 40 - F for its equivalent value T. Making this substitution into the dollar<BR>\n" );
document.write( "equation we get:<BR>\n" );
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document.write( "2(40 - F) + 5F = 146<BR>\n" );
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document.write( "Doing the distributed multiplication on the left side results in:<BR>\n" );
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document.write( "80 - 2F + 5F = 146<BR>\n" );
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document.write( "The two terms containing F (the terms are -2F and + 5F) combine to give 3F, which reduces the<BR>\n" );
document.write( "equation to:<BR>\n" );
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document.write( "80 + 3F = 146<BR>\n" );
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document.write( "Get rid of the 80 on the left side by subtracting 80 from both sides. This further reduces<BR>\n" );
document.write( "the equation to:<BR>\n" );
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document.write( "3F = 66<BR>\n" );
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document.write( "Solve for F by dividing both sides of this equation by 3 to get:<BR>\n" );
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document.write( "F = 22<BR>\n" );
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document.write( "This tells you that 22 five dollar coupons were purchased. <BR>\n" );
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document.write( "Since a total of 40 coupons were bought, this means that the number of $2 coupons was<BR>\n" );
document.write( "40 - 22 or 18.<BR>\n" );
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document.write( "Let's check the money spent. If 22 coupons were purchased at $5 each, a total of  $110 was spent<BR>\n" );
document.write( "(from $5 times 22).<BR>\n" );
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document.write( "And if 18 coupons were purchased at $2 each, a total of $36 was spent for these coupons. <BR>\n" );
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document.write( "This means that the total amount spent on coupons was $110 + $36 and that does total to $146 <BR>\n" );
document.write( "just as it should.  <BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
document.write( ". </SPAN>\n" );
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