document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120448>Question 120448</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88274 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=88274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first sentence of the problem indicates that you are looking for two numbers. It also tells<BR>\n" );
document.write( "you that there is a larger number (let's call it L) and as smaller number (let's call it S).<BR>\n" );
document.write( "Finally, it tells you that 3 times the larger (3*L) is equal to 4 times the smaller (4*S).<BR>\n" );
document.write( "In equation form this can be written as:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "3*L = 4*S<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The sum of the numbers is 21. Therefore, another equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L + S = 21<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's solve these two equations by substitution. We can start by solving the second equation<BR>\n" );
document.write( "for L by subtracting S from both sides to leave just L by itself on the left side. When<BR>\n" );
document.write( "you subtract S from both sides, the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L = 21 - S<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now let's substitute the right side of this equation for L in the first equation that we wrote.<BR>\n" );
document.write( "The first equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "3*L = 4*S<BR>\n" );
document.write( ".<BR>\n" );
document.write( "substituting 21 - S for L changes the equation to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "3*(21 - S) = 4*S<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Do the distributed multiplication on the left side by multiplying 3 times each of the terms<BR>\n" );
document.write( "in the parentheses. 3 times 21 is 63 and 3 times -S is - 3*S. This changes the left side and<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "63 - 3*S = 4*S<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the -3*S on the left side by adding +3*S to both sides. On the left side, this <BR>\n" );
document.write( "addition cancels the -3*S and on the right side the 3*S and 4*S add to give 7*S. So the <BR>\n" );
document.write( "changed equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "63 = 7*S<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for S by dividing both sides of the equation by 7. This makes the answer for S:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "S = 63/7 = 9<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now you know that the smaller number is 9. And since the total of the two numbers is<BR>\n" );
document.write( "21, the larger number is 21 - 9 = 12.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check: 3 times the larger number is 3*12 = 36. And 4 times the smaller number is 4*9 = 36.<BR>\n" );
document.write( "This means that 3*L = 4*S<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And L + S is 12 + 9 and that does equal 21, just as it should.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Therefore, the answers of 12 and 9 satisfy the problem and are, therefore, the correct answers.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );