document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170013>Question 1170013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> fourteen articles are bought. Some cost $2.00 each and the remainder cost $2.25 each.If the total amount spend is $30, how many of each article are bought </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794884 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=794884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) Using formal algebra....<br><BR>\n" );
document.write( "x = # articles at $2 each<BR>\n" );
document.write( "(14-x) = # articles at $2.25 each<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282.00%29%2B%2814-x%29%282.25%29+=+30.00 ALIGN=MIDDLE  ALT=\"x%282.00%29%2B%2814-x%29%282.25%29+=+30.00\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra.<br><BR>\n" );
document.write( "You should certainly know how to set up and solve the problem like that, or in another similar way, using formal algebra.<br><BR>\n" );
document.write( "If a formal algebraic solution is not required (for example, in a timed math competition where getting an answer as fast as possible is desired), there are many other ways to solve the problem.<br><BR>\n" );
document.write( "(2) Informally, using logical reasoning and some simple arithmetic....<br><BR>\n" );
document.write( "All 14 articles at $2.00 each would be $28.00, which is $2.00 short of the actual total.<BR>\n" );
document.write( "Each of the articles selling for $2.25 costs $0.25 more than one selling for $2.00.<BR>\n" );
document.write( "The number of articles selling at $2.25 each, in order to make up the additional $2.00, is $2.00 divided by $0.25, which is 8.<br><BR>\n" );
document.write( "ANSWER: 8 articles at $2.25 each and 14-8=6 articles at $2.00 each.<br><BR>\n" );
document.write( "CHECK: 8(2.25) + 6(2.00  = 18+12 = 30<br><BR>\n" );
document.write( "(3) And yet another solution using logical reasoning....<br><BR>\n" );
document.write( "The total cost is an even whole dollar amount; and the total cost of any number of $2.00 items will be an even whole dollar amount.<BR>\n" );
document.write( "So the total cost of the items at $2.25 each must be an even whole dollar amount.<BR>\n" );
document.write( "The only number of items (less than 14) at $2.25 each for which the total is an even whole number of dollars is 8: 8($2.25) = $18.<br><BR>\n" );
document.write( "So there must be 8 items at $2.25 each and 14-8=6 items at $2 each.<br><BR>\n" );
document.write( " </SPAN>\n" );
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