document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170240>Question 1170240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ms. Shute ordered lunch for all the math teachers. The food was ordered from yummies and the choices were chicken sandwich meals for $3.63 or hamburger meals for $2.75. Michelle ordered a total of 15 meals. The ticket was $50.05. How many chicken sandwich meals were purchased? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795094 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</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=795094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You can of course practice using formal algebra to solve problems to get the answer to the problem.  And since this problem is presumably from a course in basic algebra, you should understand how to set up and solve the problem that way.<br><BR>\n" );
document.write( "But part of the purpose of studying mathematics is to develop problem solving skills in general.<br><BR>\n" );
document.write( "You can get some good practice at that by solving this problem with logical reasoning and a bit of mental arithmetic.<br><BR>\n" );
document.write( "Here is a quick solution without formal algebra.<br><BR>\n" );
document.write( "(1) The average cost is about $50/15 = $10/3, or about $3.33; that is closer to $3.63 than it is to $2.75.  So more chicken sandwich meals than hamburger meals were ordered.<br><BR>\n" );
document.write( "(2) The total cost was $50.05, which is a multiple of 5 cents.  The cost of each hamburger meal, $2.75, was also a multiple of 5 cents; so the total cost of the hamburger meals was a multiple of 5.<br><BR>\n" );
document.write( "That means the total cost of the chicken sandwich meals must be a multiple of 5; and since the cost of each one is $3.63, the number of chicken sandwich meals must be a multiple of 5.<br><BR>\n" );
document.write( "Putting (1) and (2) together, with a total of 15 meals being ordered, the answer has to be 10 chicken sandwich meals and 5 hamburger meals.<br><BR>\n" );
document.write( "ANSWER: 10 chicken sandwich meals (and 5 hamburger meals)<br><BR>\n" );
document.write( "CHECK: 10(3.63)+5(2.75) = 36.30+13.75 = 50.05<br><BR>\n" );
document.write( "For a typical setup using formal algebra....<br><BR>\n" );
document.write( "x = # of chicken sandwich meals<BR>\n" );
document.write( "15-x = # of hamburger meals<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283.63%29%28x%29%2B%282.75%29%2815-x%29+=+50.05 ALIGN=MIDDLE  ALT=\"%283.63%29%28x%29%2B%282.75%29%2815-x%29+=+50.05\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra....<br><BR>\n" );
document.write( "(But you can see the solution is going to take much more work than the one above using logical reasoning....)<br><BR>\n" );
document.write( " </SPAN>\n" );
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