document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=487759>Question 487759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello i have 2 questions.\r<BR>\n" );
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document.write( "A mechanics hourly wage is 4 times her helpers. They were paid a total of 208$ for a job on which the mechanic worked 5 hours and the helper worked 6 hours. Find the hourly wage of the helper.\r<BR>\n" );
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document.write( "A postal clerk sold a total of 25 stamps for 10.80. Some were worth 40cents and others were worth 45cents. Find the number of each sold. \r<BR>\n" );
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document.write( "it would be great if you guys also showed me the work so I can understand how to answer these questions.\r<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 #333128 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first problem:<BR>\n" );
document.write( "a mechanic's hourly wage is 4 times the helper's.<BR>\n" );
document.write( "total job paid $208.<BR>\n" );
document.write( "mechanic worked 5 hours and the helper worked 6 hours.<BR>\n" );
document.write( "let x = the helper's pay per hour.<BR>\n" );
document.write( "then 4x = the mechanic's pay per hour.<BR>\n" );
document.write( "general formula used is hourly wage * number of hours to do the job = total cost of the job.<BR>\n" );
document.write( "let r = hourly wage and t = number of hours to do the job  and c = total cost of the job and the formula becomes:<BR>\n" );
document.write( "r * t = c<BR>\n" );
document.write( "the hourly wage is x for the helper and 4x for the mechanic.<BR>\n" );
document.write( "the total cost of the job is $208.00<BR>\n" );
document.write( "the time required to do the is 5 hours for the mechanic and 6 hours for the helper.<BR>\n" );
document.write( "the formula becomes:<BR>\n" );
document.write( "(4x * 5) + (x * 6) = $208.00<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "20x + 6x = $208.00 which becomes:<BR>\n" );
document.write( "26x = $208<BR>\n" );
document.write( "divide both sides of this equation by 26 to get:<BR>\n" );
document.write( "x = $208.00 / 26 = $8.00<BR>\n" );
document.write( "the helper's hourly wage is $8.00 per hour.<BR>\n" );
document.write( "the mechanic's hourly wage is $32.00 per hour.<BR>\n" );
document.write( "5 * 32 = $160.00<BR>\n" );
document.write( "6 * 8 = $48.00<BR>\n" );
document.write( "$160.00 + $48.00 = $208.00\r<BR>\n" );
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document.write( "second problem:<BR>\n" );
document.write( "25 stamps sold for $10.80<BR>\n" );
document.write( "some were worth 40 cents<BR>\n" );
document.write( "some were worth 45 cents<BR>\n" );
document.write( "how many of each were sold.<BR>\n" );
document.write( "total sold was 1080 cents<BR>\n" );
document.write( "x is the number of 40 cent stamps that were sold.<BR>\n" );
document.write( "y is the number of 45 cent stamps that were sold.<BR>\n" );
document.write( "x + y = 25<BR>\n" );
document.write( "this means that the total of x and y stamps came out to be 25.<BR>\n" );
document.write( "40x + 45y = 1080<BR>\n" );
document.write( "this means that the total money from 40 cent stamps and the total money from 45 cent stamps equaled a total of 1080 cents .<BR>\n" );
document.write( "you need to solve these 2 equations simultaneously to get your answer.<BR>\n" );
document.write( "you can do that by substitution or elimination or by graphing.<BR>\n" );
document.write( "we'll do it by elimination so you can see how that process works.<BR>\n" );
document.write( "your equations are:<BR>\n" );
document.write( "x + y = 25 (equation 1)<BR>\n" );
document.write( "40x + 45y = 1080 (equation 2)<BR>\n" );
document.write( "multiply both sides of equation 1 by 40 to get:<BR>\n" );
document.write( "40x + 40 = 1000 (equation 3 which equals equation 1 multiplied by 40)<BR>\n" );
document.write( "40x + 45y = 1080 (equation 2)<BR>\n" );
document.write( "subtract equation 3 from equation 2 to get:<BR>\n" );
document.write( "5y = 80<BR>\n" );
document.write( "divide both sides of this equation by 5 to get:<BR>\n" );
document.write( "y = 16<BR>\n" );
document.write( "substitute for y in equation 1 to get:<BR>\n" );
document.write( "x + 16 = 25<BR>\n" );
document.write( "subtract 16 from both sides of this equation to get:<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "your answer should be:<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( "y = 16<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "the number of 40 cent stamps is 9.<BR>\n" );
document.write( "the number of 45 cent stamps is 16.<BR>\n" );
document.write( "substitute these values for x and y in the second equation to get:<BR>\n" );
document.write( "40x + 45y = 1080 becomes:<BR>\n" );
document.write( "40*9 + 45*16 = 1080 which becomes:<BR>\n" );
document.write( "360 + 720 = 1080 which becomes:<BR>\n" );
document.write( "1080 = 1080<BR>\n" );
document.write( "this confirms the values for x and y are good. <BR>\n" );
document.write( "both equations have been solved simultaneously which means the same value of x and the same value of y is a solution to both equations.<BR>\n" );
document.write( "that's your answer.<BR>\n" );
document.write( "number of 40 cent stamps is equal to 9.<BR>\n" );
document.write( "number of 45 cent stamps is equal to 16.\r<BR>\n" );
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