document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3576>Question 3576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If w, x, y, and z are on-negative integers, each less than 3, and w(33) + x(32) + y(3) + z = 34, then w+z=<BR>\n" );
document.write( "(A) 0<BR>\n" );
document.write( "(B) 1<BR>\n" );
document.write( "(C) 2<BR>\n" );
document.write( "(D) 3<BR>\n" );
document.write( "(E) 4<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1598 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=1598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  First of all, I think you should type the given equation as<BR>\n" );
document.write( "  33 w + 32 x + 3y + z= 34,\r<BR>\n" );
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document.write( " Since w & x are non-negative integers,<BR>\n" );
document.write( " both w and x cannot be greater than 0.<BR>\n" );
document.write( " In other words, one of w and x must be 0.\r<BR>\n" );
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document.write( " When w =0, we have 32 x + 3 y + z = 34.<BR>\n" );
document.write( " If x = 0,then 3y+z = 34.<BR>\n" );
document.write( " But both y & z are less than 3, so 3y + z <= 3*2 + 2 = 8.<BR>\n" );
document.write( " And, we see that 3y+z = 34 is invalid and so x must be 1.<BR>\n" );
document.write( " Then we obtain 3y + z = 2.<BR>\n" );
document.write( " But,  3y+z = 2 implies y = 0 and z = 2.<BR>\n" );
document.write( " This shows w+z = 2 when w = 0.\r<BR>\n" );
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document.write( " When x = 0, we have 33 w + 3y + z = 34.<BR>\n" );
document.write( " 0<= y,z < 3 implies  w =1 and so z = 1<BR>\n" );
document.write( " Hence, we also have w+z = 2 in this case.\r<BR>\n" );
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document.write( " Thus, we get the answer is D.<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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