document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=655017>Question 655017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Basketball team scored 87 points in 2 point  and 3 point baskets.  If the 2 point baskets had been 3 point baskets, and the 3 point baskets had been 2 points, the team would have scored 93 points.  Find how many 2 point baskets and how many 3 point baskets the team scored. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #408912 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=408912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     A Basketball team scored 87 points in 2 point and 3 point baskets. If the 2 point baskets had been 3 point baskets, and the 3 point baskets had been 2 points, the team would have scored 93 points. Find how many 2 point baskets and how many 3 point baskets the team scored.<BR>\n" );
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document.write( "Let x = number of 2-point baskets<BR>\n" );
document.write( "and y = number of 3-point baskets<BR>\n" );
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document.write( "Because we have two unknowns, we need to find two equations:<BR>\n" );
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document.write( "From: \"A Basketball team scored 87 points in 2 point and 3 point baskets.\" we get:<BR>\n" );
document.write( "2x + 3y = 87  (equation 1)<BR>\n" );
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document.write( "And from: \"If the 2 point baskets had been 3 point baskets, and the 3 point baskets had been 2 points, the team would have scored 93 points\" we get:<BR>\n" );
document.write( "2y + 3x = 93  (equation 2)<BR>\n" );
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document.write( "solve equation 1 for y:<BR>\n" );
document.write( "2x + 3y = 87<BR>\n" );
document.write( "3y = 87-2x<BR>\n" );
document.write( "y = 29-(2/3)x<BR>\n" );
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document.write( "substitute above into equation 2 to solve for x:<BR>\n" );
document.write( "2y + 3x = 93<BR>\n" );
document.write( "2(29-(2/3)x) + 3x = 93<BR>\n" );
document.write( "58-(4/3)x + 3x = 93<BR>\n" );
document.write( "-(4/3)x + 3x = 35<BR>\n" );
document.write( "-4x + 9x = 105<BR>\n" );
document.write( "5x = 105<BR>\n" );
document.write( "x = 21 (number of 2-point baskets)<BR>\n" );
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document.write( "To find number of 3-point baskets, substitute back into equation 1:<BR>\n" );
document.write( "2x + 3y = 87<BR>\n" );
document.write( "2(21) + 3y = 87<BR>\n" );
document.write( "42 + 3y = 87<BR>\n" );
document.write( "3y = 45<BR>\n" );
document.write( "y = 15\r<BR>\n" );
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document.write( " </SPAN>\n" );
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