document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192262>Question 1192262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are at the store, and are trying to remember how much bread, meat, and cheese you were supposed to buy. The bread costs $3 per loaf, the meat costs $5 per pound, and the cheese costs $2 per pound. You know that you are to buy fifteen items, that the total cost will be $51, and that you are supposed to purchase one more meat than cheese. How many meat do you need to purchase?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824174 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</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=824174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "First an informal solution using logical reasoning....<br><BR>\n" );
document.write( "(1) take away the one \"extra\" meat, leaving 14 items for a total of $46, with equal numbers of meat and cheese.<BR>\n" );
document.write( "(2) The numbers of meat and cheese are the same, and the number of items remaining is 14; that means the number of breads is even.<BR>\n" );
document.write( "(3) Since the number of breads is even, make groups of 2 breads each, with a cost of 2($3) = $6 per group.  And since the numbers of meats and cheeses are the same, make groups of one meat and one cheese, with a cost of $5+$2 = $7 per group.<BR>\n" );
document.write( "(4) So we need to make a total of $46 using groups of $6 and $7.  There is only one way to do this: 3 groups at $6 each and 4 groups at $7 each for a total of 3($6)+4($7) = $18+28 = $46.<br><BR>\n" );
document.write( "So we have 4 groups of one meat and one cheese, plus the \"extra\" meat we accounted for at the beginning; so the number of meat you are to purchase is 5.<br><BR>\n" );
document.write( "ANSWER: 5 meats<br><BR>\n" );
document.write( "CHECK: 6($3)+5($5)+4($2) = $18 + $25 + $8 = $51<br><BR>\n" );
document.write( "A formal algebraic solution is easier than the informal one....  But solving a problem like this using logical reasoning is good brain exercise.<br><BR>\n" );
document.write( "A typical formal algebraic solution....<br><BR>\n" );
document.write( "x = # of cheese<BR>\n" );
document.write( "x+1 = # of meat (one more than the number of cheese)<BR>\n" );
document.write( "15-(x+x+1) = 14-2x = # of bread (the total number of items, 15, minus the total number of meat and cheese)<br><BR>\n" );
document.write( "The total cost is $51:<br><BR>\n" );
document.write( "2x+5(x+1)+3(14-2x)=51<BR>\n" );
document.write( "2x+5x+5+42-6x=51<BR>\n" );
document.write( "x=4<br><BR>\n" );
document.write( "ANSWER: the number of meat to purchase is x+1 = 5<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );