document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87216>Question 87216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your maximum exercise heart rate M is given by the formula M = 0.85(220-a),<BR>\n" );
document.write( "where \"a\" is your age. What is the age of someone who has a maximum exercise heart rate of 133? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63179 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=63179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "M = 0.85(220 - a)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "and also given that M = 133<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Find \"a\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Method:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute 133 for M in the equation to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "133 = 0.85(220 - a)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply 0.85 times each of the quantities in the parentheses:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "133 = 0.85*220 - 0.85*a<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that 0.85 times 220 is 187. When you do that multiplication, the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "133 = 187 - 0.85a<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next you need to get the term containing \"a\" by itself on one side of the equation, and<BR>\n" );
document.write( "everything else on the other side.  Let's begin by adding 0.85a to BOTH sides of the equation.<BR>\n" );
document.write( "When you do, the addition of 0.85a to the right side cancels the -0.85a on the right side.<BR>\n" );
document.write( "This makes the equation become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "133 + 0.85a = 187<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 133 from both sides to get rid of it on the left side.  When you subtract<BR>\n" );
document.write( "133 the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0.85a = 187 - 133 <BR>\n" );
document.write( ".<BR>\n" );
document.write( "The subtraction on the right side results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0.85a = 54<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Divide both sides by the multiplier of \"a\" to solve for \"a\". When you do that the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "a = 54/0.85 <BR>\n" );
document.write( ".<BR>\n" );
document.write( "and the right side is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "a = 63.5294<BR>\n" );
document.write( ".<BR>\n" );
document.write( "which tells you that at the age of 63.5 years the maximum rate of heart exercise is 133.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can check this by substituting 63.5 into the original equation to find that:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "M = 0.85(220 - 63.5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract the two numbers in parentheses to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "M = 0.85(156.5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "do the multiplication and the result is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "M = 133.025<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The slight difference is due to rounding off the number of years. So the answer we got in<BR>\n" );
document.write( "this checking work is equal to the heart rate specified by the problem ... 133.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand how to work the problem.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );