document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161592>Question 161592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. find three consecutive even integers whose sum is 42.<BR>\n" );
document.write( "2. the difference of the squares of the digits of a two digit positive number is <BR>\n" );
document.write( "   27. If the digits are reversed in order and the resulting number is subtracted <BR>\n" );
document.write( "   from the original number, the difference is also 27.what is the original <BR>\n" );
document.write( "   number?<BR>\n" );
document.write( "3.A's rate of doing work is three times of B. On a given day, A & B work together<BR>\n" );
document.write( "  for 4 hrs.;B is called away and S finishes the rest of the job in 2 hrs. How <BR>\n" );
document.write( "  long would it take B to do the complete job alone?<BR>\n" );
document.write( "4.Peter can run around a 400m tract in 65 sec. How long does it take for John to <BR>\n" );
document.write( "  run the 400m if he meets Peter in 35 sec.After they start together in a race <BR>\n" );
document.write( "  around the tract in opposite direction?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119143 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. find three consecutive even integers whose sum is 42.<BR>\n" );
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document.write( "x + (x+2) + (x+4) = 42<BR>\n" );
document.write( "3x + 6 = 42<BR>\n" );
document.write( "3x = 42 - y<BR>\n" );
document.write( "3x = 36<BR>\n" );
document.write( "x = 12<BR>\n" );
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document.write( "2. The difference of the squares of the digits of a two digit positive number<BR>\n" );
document.write( " is 27. If the digits are reversed in order and the resulting number is<BR>\n" );
document.write( " subtracted from the original number, the difference is also 27.<BR>\n" );
document.write( " what is the original number?<BR>\n" );
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document.write( "Let the number = 10x + y<BR>\n" );
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document.write( "\"The difference of the squares of the digits of a two digit positive number<BR>\n" );
document.write( " is 27.<BR>\n" );
document.write( "y^2 - x^2 = 27<BR>\n" );
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document.write( "\"If the digits are reversed in order and the resulting number is<BR>\n" );
document.write( " subtracted from the original number, the difference is also 27.\"<BR>\n" );
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document.write( "10y + x - (10x + y) = 27<BR>\n" );
document.write( "10y + x - 10x - y = 27<BR>\n" );
document.write( "10y - y - 10 + x = 27<BR>\n" );
document.write( "9y - 9x = 27<BR>\n" );
document.write( "Simplify, divide equation by 9<BR>\n" );
document.write( "y - x = 3<BR>\n" );
document.write( "y = (x + 3)<BR>\n" );
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document.write( "Substitute this for y in the 1st equation, find x<BR>\n" );
document.write( "(x+3)^2 - x^2 = 27<BR>\n" );
document.write( "(x^2 + 6x + 9) - x^2 = 27<BR>\n" );
document.write( "x^2 - x^2 + 6x + 9 = 27<BR>\n" );
document.write( "6x = 27 - 9<BR>\n" );
document.write( "6x = 18<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "y = 3 + 3<BR>\n" );
document.write( "y = 6<BR>\n" );
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document.write( "Our number is 36; Check it: 63 - 36 = 27<BR>\n" );
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document.write( "3. A's rate of doing work is three times of B. On a given day, A & B work<BR>\n" );
document.write( " together for 4 hrs; B is called away and S finishes the rest of the job<BR>\n" );
document.write( " in 2 hrs. How long would it take B to do the complete job alone?<BR>\n" );
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document.write( "Where did S come from (a relative perhaps?)  I assume you mean A.<BR>\n" );
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document.write( "Let x = time required by A to do the job alone<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "Let 3x = time required for B to do the job alone. (works 1/3 as fast as A)<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "The given information tells that A worked 6 hrs, and B worked 4 hrs:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fx ALIGN=MIDDLE  ALT=\"6%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%283x%29 ALIGN=MIDDLE  ALT=\"4%2F%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by 3x, results<BR>\n" );
document.write( "3(6) + 4 = 3x<BR>\n" );
document.write( "18 + 4 = 3x<BR>\n" );
document.write( "22 = 3x<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2F3 ALIGN=MIDDLE  ALT=\"22%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 7<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs, A working alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3(7<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = 22 hrs B working alone<BR>\n" );
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document.write( "Check solution on Calc: 6/7.33 + 4/22 = 1.000; confirms our solution<BR>\n" );
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document.write( "4.Peter can run around a 400m tract in 65 sec. How long does it take for John<BR>\n" );
document.write( " to run the 400m if he meets Peter in 35 sec. After they start together in a<BR>\n" );
document.write( " race around the tract in opposite direction? ?<BR>\n" );
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document.write( "When they meet, they will have traveled a total of 400 meters in 35 seconds<BR>\n" );
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document.write( "Find Peter's speed in meters/sec: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2F65 ALIGN=MIDDLE  ALT=\"400%2F65\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.154 m/sec<BR>\n" );
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document.write( "Let s = John's speed in m/sec<BR>\n" );
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document.write( "Write a dist equation; Dist = time * speed<BR>\n" );
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document.write( "35s + 35(6.154) = 400<BR>\n" );
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document.write( "35s + 215.39 = 400<BR>\n" );
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document.write( "35s = 400 - 215.39<BR>\n" );
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document.write( "35s = 184.61<BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=184.61%2F35 ALIGN=MIDDLE  ALT=\"184.61%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = 5.275 m/sec is John's speed<BR>\n" );
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document.write( "Find time for John to run 400 m: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2F5.275 ALIGN=MIDDLE  ALT=\"400%2F5.275\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 75.83 sec to run 400 m<BR>\n" );
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document.write( "Check solution: <BR>\n" );
document.write( "35 * 5.275 = 184.625 m<BR>\n" );
document.write( "35 * 6.154 = 215.39<BR>\n" );
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document.write( "Total dist = 400.0 <BR>\n" );
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document.write( "Do you have any questions about these?  </SPAN>\n" );
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