document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206119>Question 1206119</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Haresh gave 40% of his money and an additional $5 to Bob. He gave 75% of his remaining money and an additional $6 to Karen. The amount of money haresh had at the end was $44 less than what he gave to Karen. Find the amount haresh gave to Bob. <BR>\n" );
document.write( "This is word for word from my sons textbook.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843359 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=843359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "A = amount Haresh starts with<BR>\n" );
document.write( "B = amount Haresh has leftover after giving some amount to Bob (before giving anything to Karen)<BR>\n" );
document.write( "C = amount Haresh has leftover after giving some amount to Karen (and Bob previously)\r<BR>\n" );
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document.write( "In other words, Haresh will have bank balances of A,B, and C in that order after giving to Bob first and then Karen next.\r<BR>\n" );
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document.write( "0.4A+5 = amount given to Bob<BR>\n" );
document.write( "B = A - (0.4A+5) <BR>\n" );
document.write( "B = A - 0.4A - 5<BR>\n" );
document.write( "B = 0.6A - 5\r<BR>\n" );
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document.write( "0.75B + 6 = amount given to Karen<BR>\n" );
document.write( "C = B - (0.75B+6)<BR>\n" );
document.write( "C = B - 0.75B - 6<BR>\n" );
document.write( "C = 0.25B - 6\r<BR>\n" );
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document.write( "C = (amount given to Karen) - 44<BR>\n" );
document.write( "C = (0.75B + 6) - 44<BR>\n" );
document.write( "C = 0.75B - 38\r<BR>\n" );
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document.write( "We determine that<BR>\n" );
document.write( "C = 0.25B - 6<BR>\n" );
document.write( "and<BR>\n" );
document.write( "C = 0.75B - 38\r<BR>\n" );
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document.write( "Equate the right hand sides so we can determine B.<BR>\n" );
document.write( "0.75B - 38 = 0.25B - 6<BR>\n" );
document.write( "0.75B - 0.25B = -6 + 38<BR>\n" );
document.write( "0.50B = 32<BR>\n" );
document.write( "B = 32/0.50<BR>\n" );
document.write( "B = 64<BR>\n" );
document.write( "Haresh will have $64 after giving some amount to Bob, but this is before Haresh gives any money to Karen.\r<BR>\n" );
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document.write( "Use this value of B to find A.<BR>\n" );
document.write( "B = 0.6A - 5<BR>\n" );
document.write( "64 = 0.6A - 5<BR>\n" );
document.write( "64+5 = 0.6A<BR>\n" );
document.write( "69 = 0.6A<BR>\n" );
document.write( "A = 69/0.6<BR>\n" );
document.write( "A = 115<BR>\n" );
document.write( "Haresh started with $115.\r<BR>\n" );
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document.write( "Let's use the value of B to find C.<BR>\n" );
document.write( "C = 0.25B - 6<BR>\n" );
document.write( "C = 0.25*64 - 6<BR>\n" );
document.write( "C = 16 - 6<BR>\n" );
document.write( "C = 10<BR>\n" );
document.write( "Haresh ends up with $10 after giving some amounts to Bob and Karen.<BR>\n" );
document.write( "Or we can compute it like this:<BR>\n" );
document.write( "C = 0.75B - 38<BR>\n" );
document.write( "C = 0.75*64 - 38<BR>\n" );
document.write( "C = 48 - 38<BR>\n" );
document.write( "C = 10<BR>\n" );
document.write( "Or like this:<BR>\n" );
document.write( "C = 0.15A - 7.25<BR>\n" );
document.write( "C = 0.15*115 - 7.25<BR>\n" );
document.write( "C = 17.25 - 7.25<BR>\n" );
document.write( "C = 10<BR>\n" );
document.write( "You only need to use one equation to find C, but it helps to check multiple equations to ensure we get the same result each time.\r<BR>\n" );
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document.write( "To summarize,<BR>\n" );
document.write( "A = 115 = amount Haresh started with<BR>\n" );
document.write( "B = 64 = amount Haresh has left after he gives some money to Bob (before Karen gets any money)<BR>\n" );
document.write( "C = 10 = amount Haresh has left after giving some money to Karen (Bob already got his gift)\r<BR>\n" );
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document.write( "The gap from A to B is A-B = 115-64 = <font color=red>51 dollars</font> which is the amount Haresh gave to Bob.<BR>\n" );
document.write( "Note 40% of 115 = 0.40*115 = 46 dollars is given to Bob and then another extra $5, so that's 46+5 = <font color=red>51 dollars</font> total given to Bob.\r<BR>\n" );
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document.write( "The gap from B to C is B-C = 64-10 = 54 dollars which is the amount given to Karen.<BR>\n" );
document.write( "75% of what Haresh has left (the $64) is 0.75*64 = 48 dollars is given to Karen, in addition to another extra $6. So she gets 48+6 = 54 dollars.<BR>\n" );
document.write( "Haresh ultimately ends up with 64 - 54 = 10 dollars.<BR>\n" );
document.write( "Notice $10 is $44 less than what he gave to Karen (she got $54).<BR>\n" );
document.write( "This helps us verify the solution is correct.\r<BR>\n" );
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document.write( "Another way to confirm the answer is to use a spreadsheet as shown here<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://docs.google.com/spreadsheets/d/145sUDhOxWyWCcL4awl6FTGExxgmIxKLaN8802JNTDZQ/edit?usp=sharing\">https://docs.google.com/spreadsheets/d/145sUDhOxWyWCcL4awl6FTGExxgmIxKLaN8802JNTDZQ/edit?usp=sharing</a><BR>\n" );
document.write( "You do not need a Google account to access this spreadsheet. <BR>\n" );
document.write( "Click any cell to see what formula I used for it. The formula bar is at the top.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>$51</font><BR>\n" );
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