document.write( "Question 816678: Please Help..
\n" ); document.write( "Five years ago, Roel was three times as old as his brother, Tony. In 10 years, he will be 10 years older than Tony. Find their present ages. \n" ); document.write( "
Algebra.Com's Answer #491659 by Theo(13342)\"\" \"About 
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let x equal roel's age now.
\n" ); document.write( "let y = tony's age now.
\n" ); document.write( "five years ago, roel was x-5 years old.
\n" ); document.write( "five years ago, tony was y-5 years old.
\n" ); document.write( "five years ago, roel was 3 times as old as tony.
\n" ); document.write( "this means that:
\n" ); document.write( "(x-5) = 3 * (y-5)
\n" ); document.write( "simplify this to get:
\n" ); document.write( "x-5 = 3y - 15
\n" ); document.write( "add 5 to both sides of this equation to get:
\n" ); document.write( "x = 3y - 10
\n" ); document.write( "you now have the value of x in terms of y.
\n" ); document.write( "you're still not there yet.
\n" ); document.write( "you are also told that in 10 years raul will be 10 years older than tony.
\n" ); document.write( "if raul is x years old now, then raul will be x + 10 years old in 10 years.
\n" ); document.write( "if tony is y years old now, then tony will be y + 10 years old in 10 years.
\n" ); document.write( "in 10 years, raul will be 10 years older than tony.
\n" ); document.write( "this means that:
\n" ); document.write( "x + 10 = (y + 10) + 10 which can be simplified to:
\n" ); document.write( "x + 10 = y + 20
\n" ); document.write( "you can solve for x again to get:
\n" ); document.write( "x = y + 10
\n" ); document.write( "you now have 2 equations for x.
\n" ); document.write( "the first equation is:
\n" ); document.write( "x = 3y - 10
\n" ); document.write( "the second equaton is:
\n" ); document.write( "x = y + 10
\n" ); document.write( "since 2y-10 and y+10 are both equal to x, you can set them equal to each other and solve for y.
\n" ); document.write( "you get:
\n" ); document.write( "3y-10 = y+10
\n" ); document.write( "subtract y from both equations and add 10 to both sides of this equation to get:
\n" ); document.write( "2y = 20
\n" ); document.write( "divide both sides of this equation by 2 to get:
\n" ); document.write( "y = 10
\n" ); document.write( "now that you know that y is equal to 10, you can solve for x in either equation of:
\n" ); document.write( "x = y + 10 or x = 3y - 10
\n" ); document.write( "if you use x = y + 10, you get x = 10 + 10 = 20
\n" ); document.write( "if you use x = 3y - 10, you get x = 30 - 10 = 20
\n" ); document.write( "either equation will get you that x = 20.
\n" ); document.write( "your solution is:
\n" ); document.write( "x = 20
\n" ); document.write( "y = 10
\n" ); document.write( "5 years ago, x = 15 and y = 5 which means that x equals to 3*y.
\n" ); document.write( "10 years from now, x = 30 and y = 20 which means that x equals y + 10.
\n" ); document.write( "the equations are both satisfied and the solution is good.\r
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\n" ); document.write( "\n" ); document.write( "there are several ways to solve this.
\n" ); document.write( "i used substitution.
\n" ); document.write( "you can also solve by elimination.
\n" ); document.write( "you can also solve by graphing.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the whole idea is that you wind up with 2 equations that need to be solved simultaneously to arrive at a solution.\r
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