document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160158>Question 160158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi-I was trying to help my 6th grader with his math homework. Many years since I have done any, the problem was from a work sheet. A Frog is in a 10 foot well, climbs 3 feet during the day and slides back 2 feet at night. At what point will the frog make it to the 10 foot level and be able to crawl out? I thought the answer would be 8 days, but I did not have a formula to use. Would you please help out a frustrated dad?? Thanks for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118214 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> goes up 3 in the day and goes down 2 in the night.<BR>\n" );
document.write( "at the end of the first day there's a gain of 3.<BR>\n" );
document.write( "at the end of each succeeding day there's a gain of 1 (loss of 2 during the night).<BR>\n" );
document.write( "end of day 1 he's up 3<BR>\n" );
document.write( "end of day 2 he's up 4<BR>\n" );
document.write( "end of day 3 he's up 5<BR>\n" );
document.write( "end of day 7 he's up 9<BR>\n" );
document.write( "end of day 8 he's up 10<BR>\n" );
document.write( "you're correct.<BR>\n" );
document.write( "number of days is 8.<BR>\n" );
document.write( "now the formula.<BR>\n" );
document.write( "let x be the number of days needed to get out of the well.<BR>\n" );
document.write( "formula looks like it will be<BR>\n" );
document.write( "(x-1)*(3-2) + 3 = 10<BR>\n" );
document.write( "what this says is that you have x-1 days where the net gain was only 1.<BR>\n" );
document.write( "that would be the loss of 2 the night before plus the gain of 3 during the day.<BR>\n" );
document.write( "the + 3 means you got a net gain of 3 the first day.<BR>\n" );
document.write( "so (x-1)*(3-2) + 3 = 10<BR>\n" );
document.write( "solving you get<BR>\n" );
document.write( "(x-1)(1) + 3 = 10<BR>\n" );
document.write( "x - 1 + 3 = 10<BR>\n" );
document.write( "x - 1 = 7<BR>\n" );
document.write( "x = 8<BR>\n" );
document.write( "i must admit i didn't think about it correctly the first time i looked at it.<BR>\n" );
document.write( "congratulations on good logic.\r<BR>\n" );
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