document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162699>Question 1162699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Extreme Rock Climbing Club planned a climbing expedition.  The total cost was $3200, which was to be divided equally among the members going.  Prior to the trip, 15 members decided not to go.  If the cost per person increased by $48, how many people went on the expedition? </SPAN>\n" );
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document.write( "A setup for solving the problem using formal algebra....<br><BR>\n" );
document.write( "Let x be the number who went on the expedition.  Then x+15 is the number that were originally going to go.<br><BR>\n" );
document.write( "The cost per person originally was 3200/(x+15); the cost now is 3200/x.<br><BR>\n" );
document.write( "We are told the difference between those two costs is $48:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3200%2Fx-3200%2F%28x%2B15%29+=+48 ALIGN=MIDDLE  ALT=\"3200%2Fx-3200%2F%28x%2B15%29+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply by the common denominator x(x+15) to clear fractions:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3200%28x%2B15%29-3200%28x%29+=+48%28x%29%28x%2B15%29 ALIGN=MIDDLE  ALT=\"3200%28x%2B15%29-3200%28x%29+=+48%28x%29%28x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48000+=+48%28x%5E2%2B15x%29 ALIGN=MIDDLE  ALT=\"48000+=+48%28x%5E2%2B15x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+=+x%5E2%2B15x ALIGN=MIDDLE  ALT=\"1000+=+x%5E2%2B15x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B15x-1000+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B15x-1000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To solve that by factoring, you need to find two integers with a difference of 15 whose product is 1000.  If your mental math is good, you should find 25 and 40 work.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B40%29%28x-25%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B40%29%28x-25%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Ignore the negative solution, since it makes no sense in the problem.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+25 ALIGN=MIDDLE  ALT=\"x+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 25 people went on the trip.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "3200/25 = 128<BR>\n" );
document.write( "3200/40 = 80<BR>\n" );
document.write( "128-80 = 48<br><BR>\n" );
document.write( "You should know how to set up and solve the problem like that, using formal algebra.<br><BR>\n" );
document.write( "But if a formal algebraic solution is  not required, you can solve the problem much faster if your mental math is good.<br><BR>\n" );
document.write( "In the original problem, you need to find two different pairs of two positive integers that give a product of 3200; you are looking to have the differences between the numbers in the two pairs equal to 15 and 48.<br><BR>\n" );
document.write( "A bit of playing around with the numbers will find<BR>\n" );
document.write( "40*80 = 3200<BR>\n" );
document.write( "25*128 = 3200<br><BR>\n" );
document.write( "The difference between 40 and 25 is 15; the difference between 80 and 128 is 48.  So those numbers are the ones we want.<br><BR>\n" );
document.write( "So originally there were 40 members paying $80 each, and in the end there were 25 members paying $128 each.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );