document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=736146>Question 736146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A basketball player scored 18 times during one game. He scored a total of 30 points, which consists of 1 point free throws and 2 point baskets. How many one point free throws did he make? How many 2 point baskets did he make? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852639 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13258)</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=852639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have received two responses showing different ways of solving the problem.  Briefly summarized, here are those two methods.<br><BR>\n" );
document.write( "First tutor (set up the problem using only one variable)....<BR>\n" );
document.write( "x = # of 1-point shot, so (18-x) = # of 2-point shots.<BR>\n" );
document.write( "The point total is 30, so x(1)+2(18-x) = 30.<BR>\n" );
document.write( "Solve that equation to find the answer.<br><BR>\n" );
document.write( "Second tutor (set up the problem using two variables and two equations and solve using substitution)....<BR>\n" );
document.write( "x = # of 1-point shots; y = # of 2-points shots.<BR>\n" );
document.write( "The total number of shots is 18, so x+y = 18.<BR>\n" );
document.write( "The point total is 30, so x(1)+2(y) = 30.<BR>\n" );
document.write( "Solve the first equation for x: x = 18-y.<BR>\n" );
document.write( "Substitute \"18-y\" for \"x\" in the second equation, giving x(1)+2(18-x) = 30.<BR>\n" );
document.write( "At that point the equation to solve is the same as in the solution from the first tutor, so solving the problem from there is the same.<br><BR>\n" );
document.write( "A different method for solving the problem -- which a student should also know -- is using two variables and two equations and solving the pair of equations using elimination.<BR>\n" );
document.write( "x+y = 18; x+2y = 30<BR>\n" );
document.write( "Subtract the first equation from the second, eliminating x: y = 12<BR>\n" );
document.write( "Substitute y=12 in either equation to find x = 6<br><BR>\n" );
document.write( "ANSWER: x = 6 1-point shots and y = 12 2-point shots<br><BR>\n" );
document.write( "Finally, while a student should understand and be able to use either substitution or elimination to solve the problem, it should be noted that solving the problem informally, using logical reasoning and simple arithmetic instead of formal algebra, is excellent mental exercise.<br><BR>\n" );
document.write( "For this problem, the calculations are exactly those used in the above solution using elimination. Here is how the thinking can go:<br><BR>\n" );
document.write( "(1) If all 18 shots were 2-point shots, the point total would be 18*2 = 36.<BR>\n" );
document.write( "(2) The actual point total, 30, is 6 points less than that.<BR>\n" );
document.write( "(3) Since each 1-point shot is worth 1 point less than each 2-point shot, the number of 1-point shots must have been 6.<BR>\n" );
document.write( "ANSWERS: 6 1-point shot; so 18-6 = 12 2-point shots<br><BR>\n" );
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