document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204068>Question 1204068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Julie cashed a paycheck and repaid her brother $10 that she had borrowed from him. She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. She bought a pair of running shoes for $29.45 and had $17.75 left. How much did Julie receive when she cashed her paycheck? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840078 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</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=840078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = her paycheck amount<BR>\n" );
document.write( "x-10 = what she has left over after repaying her brother<BR>\n" );
document.write( "x-10-30 = x-40 = left over amount after buying fuel\r<BR>\n" );
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document.write( "(1/2)(x-40) = 0.5x-20 = amount she has left after buying the tent\r<BR>\n" );
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document.write( "0.5x-20-29.45 = 0.5x-49.45 = amount she has left after buying the shoes\r<BR>\n" );
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document.write( "Set this equal to the stated value 17.75 so we can solve for x.<BR>\n" );
document.write( "0.5x-49.45 = 17.75<BR>\n" );
document.write( "0.5x = 17.75+49.45<BR>\n" );
document.write( "0.5x = 67.20<BR>\n" );
document.write( "2*0.5x = 2*67.20<BR>\n" );
document.write( "x = <font color=red>$134.40</font> is the answer.\r<BR>\n" );
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document.write( "Checking the answer:\r<BR>\n" );
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document.write( "start = $134.40<BR>\n" );
document.write( "repays brother = $134.40 - $10 = $124.40 left over<BR>\n" );
document.write( "buys fuel = $124.40 - $30 = $94.40 left over<BR>\n" );
document.write( "buys tent = (1/2)*($94.40) = $47.20 left over<BR>\n" );
document.write( "buys shoes = $47.20 - $29.45 = $17.75 is what she'll have left over after purchasing all the items mentioned, and repaying her brother.<BR>\n" );
document.write( "Answer is confirmed.\r<BR>\n" );
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document.write( "Another approach\r<BR>\n" );
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document.write( "She ended up with $17.75<BR>\n" );
document.write( "Add on the price of the shoes to rewind the clock so she gets that money back.<BR>\n" );
document.write( "17.75+29.45 = 47.20<BR>\n" );
document.write( "Before buying the shoes, she would have $47.20\r<BR>\n" );
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document.write( "Double this to get $94.40 when we rewind the clock further back. This is the amount she would have just before buying the tent.<BR>\n" );
document.write( "Then add on $30 to rewind further to get $124.40 to represent what she would have just before buying fuel.\r<BR>\n" );
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document.write( "Lastly, she'll take the $10 from her brother when rewinding the clock all the way back to the start point.<BR>\n" );
document.write( "$124.40+$10 = <font color=red>$134.40</font><BR>\n" );
document.write( "Basically we follow the \"check\" section shown above, but do so in reverse. <BR>\n" );
document.write( "Any time we have a subtraction, the inverse would be addition. The inverse of halving is doubling. <BR>\n" );
document.write( "This rewinding action is basically how we solve equations. \r<BR>\n" );
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document.write( "Answer: <font color=red size=4>$134.40</font><BR>\n" );
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