document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=973010>Question 973010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "I have been trying to solve a word problem, here it is:\r<BR>\n" );
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document.write( "Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?\r<BR>\n" );
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document.write( "I know that I need to turn the problem into an equation and then solve, but I can not figure out how to turn the problem into an equation\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595279 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=595279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your problem states:\r<BR>\n" );
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document.write( "Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now? \r<BR>\n" );
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document.write( "let x = evan's age now.<BR>\n" );
document.write( "let y = his sister's age now.\r<BR>\n" );
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document.write( "3 years ago, evan was one third of his sister's age.<BR>\n" );
document.write( "if x is evan's age now, then evan's age 3 years ago has to be x-3.<BR>\n" );
document.write( "if his sister is y years old now, then his sister's age 3 years ago has to be y - 3.<BR>\n" );
document.write( "3 years ago, he was one third his sister's age.<BR>\n" );
document.write( "this leads to:<BR>\n" );
document.write( "(x-3) = 1/3 * (y-3)\r<BR>\n" );
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document.write( "In a year's time, Evan's age doubled will match his sister's age.<BR>\n" );
document.write( "in one year, evan's age will be x + 1.<BR>\n" );
document.write( "in one year evan's sister's age will be y + 1.<BR>\n" );
document.write( "this leads to:<BR>\n" );
document.write( "2 * (x+1) = (y + 1)\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "x-3 = 1/3 * (y-3)<BR>\n" );
document.write( "2 * (x+1) = y+1\r<BR>\n" );
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document.write( "you can solve these two equations by any of the methods that you learend for solving two equations simultaneously.\r<BR>\n" );
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document.write( "i'll use substitution, but you can also use elimination or by graphing.\r<BR>\n" );
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document.write( "in your first equations, solve for x to get:\r<BR>\n" );
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document.write( "x = 1/3 * (y-3) + 3<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "x = 1/3 * y - 1/3 * 3 + 3<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "x = 1/3 * y - 1 + 3<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "x = 1/3 * y + 2\r<BR>\n" );
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document.write( "replace x with 1/3 * y + 2 in the second equation to get:\r<BR>\n" );
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document.write( "2 * (x+1) = y+1 becomes:<BR>\n" );
document.write( "2 * (1/3 * y + 2 + 1) = y + 1 which becomes:<BR>\n" );
document.write( "2/3 * y + 4 + 2 = y + 1 which becomes:<BR>\n" );
document.write( "2/3 * y + 6 = y + 1<BR>\n" );
document.write( "subtract 2/3 * y from both sides of this equation and subtract 1 from both sides of this equation to get:<BR>\n" );
document.write( "5 = 1/3 * y<BR>\n" );
document.write( "multiply both sides of this equation by 3 and solve for y to get:<BR>\n" );
document.write( "y = 15\r<BR>\n" );
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document.write( "go back to either of your original equations and solve for x.\r<BR>\n" );
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document.write( "your original equations are:\r<BR>\n" );
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document.write( "x-3 = 1/3 * (y-3)<BR>\n" );
document.write( "2 * (x+1) = y+1\r<BR>\n" );
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document.write( "in the first equation, replace y with 15 to get:\r<BR>\n" );
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document.write( "x-3 = 1/3 * (15-3) which becomes:<BR>\n" );
document.write( "x-3 = 1/3 * 12) which becomes:<BR>\n" );
document.write( "x-3 = 4 which becomes:<BR>\n" );
document.write( "x = 7\r<BR>\n" );
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document.write( "you now have x = 7 and y = 15.\r<BR>\n" );
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document.write( "go back to the second original equation and replace x with 7 and y with 15 to see if that equation is true.\r<BR>\n" );
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document.write( "the second original equation is:\r<BR>\n" );
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document.write( "2 * (x+1) = y+1 which becomes:<BR>\n" );
document.write( "2 * (7+1) = (15+1) which becomes:<BR>\n" );
document.write( "2 * 8 = 16 which becomes:<BR>\n" );
document.write( "16 = 16 which is true.\r<BR>\n" );
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document.write( "looks like the value of x = 7 and y = 15 is a solution to this problem.\r<BR>\n" );
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document.write( "x is evan's age.<BR>\n" );
document.write( "y is his sister's age.\r<BR>\n" );
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document.write( "go back to the original problem statements to see if these values make those statements true.\r<BR>\n" );
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document.write( "the original statements are:\r<BR>\n" );
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document.write( "Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now? \r<BR>\n" );
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document.write( "evan is 7 now and his sister is 15 now.\r<BR>\n" );
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document.write( "3 years ago he was 4 and she was 12.<BR>\n" );
document.write( "4 is equal to 1/3 * 12 so the first statement is true.\r<BR>\n" );
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document.write( "in a year's time, evan's age doubled will match his sister's age.<BR>\n" );
document.write( "in a years' time he will be 8 and you multiply that by 2 to get 16.<BR>\n" );
document.write( "in a years' time she will be 15 + 1 = 16.\r<BR>\n" );
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document.write( "values look good.\r<BR>\n" );
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document.write( "answer to the question is:\r<BR>\n" );
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document.write( "evan is 7 years old now.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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