document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205706>Question 1205706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 13. One number is 25 less than the other. Find the numbers.\r<BR>\n" );
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document.write( "The smaller number is: \r<BR>\n" );
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document.write( "The larger number is: \r<BR>\n" );
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document.write( "The perimeter of a rectangle is 124. The length is 4 less than<BR>\n" );
document.write( "5 times the width.  Find the width and length.\r<BR>\n" );
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document.write( "Width: \r<BR>\n" );
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document.write( "Length: \r<BR>\n" );
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document.write( "The measure of one of the small angles of a right triangle is 29 less than 6 times the measure of the other small angle. Find the measure of both angles.\r<BR>\n" );
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document.write( "Smallest angle: \r<BR>\n" );
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document.write( "Other non-right angle: \r<BR>\n" );
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document.write( "Jerome currently sells stoves for Gabriela's Stove Store at a salary of $16,000 plus a $10 commission for each stove he sells. Logan's Stove Store offers him a position with a salary of $13,000 plus a commission of $25 for each stove he sells. How many stoves would he need to sell for the options to be equal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842686 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=842686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 13. One number is 25 less than the other. Find the numbers.<BR>\n" );
document.write( "The smaller number is:<BR>\n" );
document.write( "The larger number is:\r<BR>\n" );
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document.write( "x is the larger number<BR>\n" );
document.write( "y is the smaller number\r<BR>\n" );
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document.write( "x + y = 13<BR>\n" );
document.write( "y = x - 25\r<BR>\n" );
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document.write( "replace y with x - 25 to get x + x - 25 = 13<BR>\n" );
document.write( "combine like terms and add 25 to both sides of the equation to get 2x = 38<BR>\n" );
document.write( "solve for x to get x = 19<BR>\n" );
document.write( "y = x - 25 means y = -6\r<BR>\n" );
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document.write( "x = 19 and y = -6 is your answer.<BR>\n" );
document.write( "-6 + 19 = 13.<BR>\n" );
document.write( "answer is confirmed to be correct.\r<BR>\n" );
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document.write( "The perimeter of a rectangle is 124. The length is 4 less than<BR>\n" );
document.write( "5 times the width. Find the width and length.<BR>\n" );
document.write( "Width:<BR>\n" );
document.write( "Length:\r<BR>\n" );
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document.write( "p = 2l + 2w<BR>\n" );
document.write( "p = 124 so the formula becomes 124 = 2l + 2w<BR>\n" );
document.write( "l = 5w - 4 so the formula becomes 124 = 2 * (5w-4) + 2w<BR>\n" );
document.write( "simplify and combine like terms to get 124 = 12w - 8<BR>\n" );
document.write( "add 8 to both sides to get 132 = 12w<BR>\n" );
document.write( "solve for w to get w = 132 / 12 = 11<BR>\n" );
document.write( "l = 4 less than 5w gets you l = 51<BR>\n" );
document.write( "dimensions are l = 51 and w = 11<BR>\n" );
document.write( "2l + 2w gets you 102 + 22 = 124<BR>\n" );
document.write( "this confirms the dimensions are correct.<BR>\n" );
document.write( "your solution is length = 51 and width = 11.\r<BR>\n" );
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document.write( "The measure of one of the small angles of a right triangle is 29 less than 6 times the measure of the other small angle. Find the measure of both angles.<BR>\n" );
document.write( "Smallest angle:<BR>\n" );
document.write( "Other non-right angle:\r<BR>\n" );
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document.write( "right triangle has one 90 degree angle and 2 angles that are each less than 90 degrees.\r<BR>\n" );
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document.write( "one of the smaller angles is x.<BR>\n" );
document.write( "the other is y.<BR>\n" );
document.write( "sum of the angles of the triangle is 180 degrees.<BR>\n" );
document.write( "subtract the 90 degree angle to get the sum of the smaller angles is 90.<BR>\n" );
document.write( "formula becomes x + y = 90<BR>\n" );
document.write( "let x = 6y - 29<BR>\n" );
document.write( "replace x with that to get 6y - 29 + y = 90<BR>\n" );
document.write( "combine like terms and add 29 to both sides to get 7y = 119<BR>\n" );
document.write( "solve for y to get y = 119/7 = 17<BR>\n" );
document.write( "x = 6y - 29 makes x = 73<BR>\n" );
document.write( "you have x = 73 and y = 17<BR>\n" );
document.write( "73 + 17 = 90 and 6 * 17 - 29 = 73 confirms the values of the angles are correct.<BR>\n" );
document.write( "x = 73 and y = 17 is your answer.\r<BR>\n" );
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document.write( "Jerome currently sells stoves for Gabriela's Stove Store at a salary of $16,000 plus a $10 commission for each stove he sells. Logan's Stove Store offers him a position with a salary of $13,000 plus a commission of $25 for each stove he sells. How many stoves would he need to sell for the options to be equal?\r<BR>\n" );
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document.write( "16000 + 10x = 13000 + 25x is the break even point.<BR>\n" );
document.write( "subtract 13000 from both sides and subtrasct 10x from both sides to get 3000 = 15x<BR>\n" );
document.write( "solve for x to get x = 3000 / 25 = 200\r<BR>\n" );
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document.write( "the options are equal when he sells 200 stoves.\r<BR>\n" );
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document.write( "at the break even point:<BR>\n" );
document.write( "16000 + 10 * 200 = 18000<BR>\n" );
document.write( "13000 + 25 * 200 = 18000\r<BR>\n" );
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document.write( "he will have made 18000 with either option.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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