document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183621>Question 183621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am currently taking Algebra 1, and need assistance with the following word problems (that use substitution, of course):\r<BR>\n" );
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document.write( "1.)Lisa and Beverly had just $5 to spend for an after-school snack. They could have bought  2 hamburgers and 1 carton of milk with no change back or 1 hamburger and 2 cartons of milk with 40 cents change back. How much does a carton of milk cost?\r<BR>\n" );
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document.write( "2.)If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you'll get $2 change. How much does each pen and each pencil cost?\r<BR>\n" );
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document.write( "3.)One number is 16 more than another. If the smaller number is subtracted from two-thirds of the larger number, the result is one-fourth of the sum of the two numbers. Find the numbers.\r<BR>\n" );
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document.write( "Thank you very much! An answer as immediate as possible would be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137836 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=137836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.)Lisa and Beverly had just $5 to spend for an after-school snack. They could have bought 2 hamburgers and 1 carton of milk with no change back or 1 hamburger and 2 cartons of milk with 40 cents change back. How much does a carton of milk cost<BR>\n" );
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document.write( "2h + c = 500 cents<BR>\n" );
document.write( "h  + 2c= 460 cents<BR>\n" );
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document.write( "Prepare for substitution:<BR>\n" );
document.write( "c = 500 -2h <BR>\n" );
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document.write( "Substitute to solve for \"h\":<BR>\n" );
document.write( "h + 2(500-2h) = 460<BR>\n" );
document.write( "h 1000 -4h = 460<BR>\n" );
document.write( "-3h = -540<BR>\n" );
document.write( "h = 180 cents = $1.80 (the price of a hamburger)<BR>\n" );
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document.write( "Substitute to solve for \"c\":<BR>\n" );
document.write( "c = 500 - 2(180)<BR>\n" );
document.write( "c = 500 - 360<BR>\n" );
document.write( "c = 140 cents = $1.40 (the price of a carton of mild)<BR>\n" );
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document.write( "2.)If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you'll get $2 change. How much does each pen and each pencil cost?<BR>\n" );
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document.write( "Equations:<BR>\n" );
document.write( "6p + m = 900 cents<BR>\n" );
document.write( "4p +2m = 800 cents<BR>\n" );
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document.write( "Prepare for substitution:<BR>\n" );
document.write( "m = 900-6p<BR>\n" );
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document.write( "Substitute to solve for \"p\":<BR>\n" );
document.write( "4p + 2(900-6p) = 800<BR>\n" );
document.write( "4p + 1800 - 12p = 800<BR>\n" );
document.write( "-8p = -1000<BR>\n" );
document.write( "p = 125 cents = $1.25 (price of a pen)<BR>\n" );
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document.write( "Substitute to solve for mechanical pencil:<BR>\n" );
document.write( "m = 900 - 6p<BR>\n" );
document.write( "m = 900 - 6(125)<BR>\n" );
document.write( "m = 900 - 750 = 150 cents = $1.50 (price of a mechanical pencil)<BR>\n" );
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document.write( "3.)One number is 16 more than another. If the smaller number is subtracted from two-thirds of the larger number, the result is one-fourth of the sum of the two numbers. Find the numbers.<BR>\n" );
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document.write( "Equations:<BR>\n" );
document.write( "x = y - 16<BR>\n" );
document.write( "(2/3)y - x = (1/4)(x+y)<BR>\n" );
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document.write( "Simplify the 2nd equation:<BR>\n" );
document.write( "8y - 12x = 3x + 3y<BR>\n" );
document.write( "15x = 5y<BR>\n" );
document.write( "x = (1/3)y<BR>\n" );
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document.write( "Substitute to solve for \"Y\":<BR>\n" );
document.write( "(1/3)y = y - 16<BR>\n" );
document.write( "(2/3)y = 16<BR>\n" );
document.write( "(1/3)y = 8<BR>\n" );
document.write( "y = 24<BR>\n" );
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document.write( "Substitute to solve for \"x\":<BR>\n" );
document.write( "x = (1/3)y = 8 <BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "  </SPAN>\n" );
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