document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471145>Question 471145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) A box with a square base and no top is to be made from a square piece of tin by cutting out 3-inch squares from each corner and folding up the sides. If the box is to hold 48 cu. in., what size of tin should be used?\r<BR>\n" );
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document.write( "2) Orlando won $200.000 in a state lottery. He first paid an income tax of 30% of the winnings and the rest he invested at 8.5% and 7% earning $10,700 interest a year. How much did he invest at each rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323187 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> box has a square base.<BR>\n" );
document.write( "box has no top.<BR>\n" );
document.write( "piece of tin is square (assumed).<BR>\n" );
document.write( "box needs to hold 48 cubic inches.<BR>\n" );
document.write( "formula for volume of this box is L*W*H = 48<BR>\n" );
document.write( "Since L = W, then the formula for the volume of this box becomes:<BR>\n" );
document.write( "S^2*H = 48<BR>\n" );
document.write( "We simply just made L = S and W = S and substituted in the volume equation.<BR>\n" );
document.write( "The equation for the volume of the box is S^2*H = 48<BR>\n" );
document.write( "Since we cut 3 inch squares from each corner of the box, then the height of our box will be 3 inches.<BR>\n" );
document.write( "Substitute this in our equation for the box and we get:<BR>\n" );
document.write( "S^2*3 = 48<BR>\n" );
document.write( "divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "S^2 = 48/3 = 16<BR>\n" );
document.write( "take the square root of each side of this equation to get:<BR>\n" );
document.write( "S = 4<BR>\n" );
document.write( "Our box will be 4 inches long by 4 inches wide by 3 inches high.<BR>\n" );
document.write( "The volume of our box will be 4*4*3 = 48 cubic inches.<BR>\n" );
document.write( "The bottom of the box is square (L = 4 and W = 4)<BR>\n" );
document.write( "It is assumed that the dimensions of the original piece of tin was:<BR>\n" );
document.write( "L = 4 + 6 = 10<BR>\n" );
document.write( "W = 4 + 6 = 10<BR>\n" );
document.write( "That means that the area of the original piece of tin was 100 square inches.<BR>\n" );
document.write( "We removed 3 inch squares from each corner which means we removed 9*4 = 36 square inches from the area of the original piece of tin.<BR>\n" );
document.write( "This left 100 - 36 = 64 square inches of tin that was used to make the open ended box.<BR>\n" );
document.write( "The surface area of the tin box is equal to the area of the bottom plus 4 times the area of each side.<BR>\n" );
document.write( "The area of the bottom is 4*4 = 16 square inches.<BR>\n" );
document.write( "The area of each side is equal to 4*3 = 12 square inches.<BR>\n" );
document.write( "16 square inches + 4*12 square inches = 16 + 48 = 64 square inches.<BR>\n" );
document.write( "That's exactly what it should be, so we're good all around.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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