document.write( "Question 224174: Paul is 12. His father is 33. How many years ago was the father 4 times as old as the son?\r
\n" ); document.write( "\n" ); document.write( "A father is 4 times as old as his daughter is now. In 20 years he will be only twice as old as his daughter. How old are the father and the daughter now? \n" ); document.write( "
Algebra.Com's Answer #167485 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
Paul is 12. His father is 33. How many years ago was the father 4 times as old as the son?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be the number of years ago when the father was 4 times as old as the son?\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 12-x be Paul's age x years ago.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 33-x be the age of Paul's father.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Then, 33-x=4(12-x) since the father was 4 times as old as the son x years ago.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Solving the equation in Step 4 yields the following steps\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=5.
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  • Graphical form: Equation \"33-x=4%2A%2812-x%29\" was fully solved.
  • Text form: 33-x=4*(12-x) simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+33-x=4%2A%2812-x%29+%29\"
    For tutors: simplify_cartoon( 33-x=4*(12-x) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+33+%29-x=4%2A%2812-x%29\".
Moved \"33\" to the right of expression
It becomes \"-x%2Bhighlight_green%28+33+%29=4%2A%2812-x%29\".
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Look at \"-x%2B33=4%2A%28highlight_red%28+12+%29-x%29\".
Moved \"12\" to the right of expression
It becomes \"-x%2B33=4%2A%28-x%2Bhighlight_green%28+12+%29%29\".
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Look at \"-x%2B33=highlight_red%28+4%2A%28-x%2B12%29+%29\".
Moved these terms to the left \"highlight_green%28+-4%2A%28-x%2B12%29+%29\"
It becomes \"-x%2B33-highlight_green%28+4%2A%28-x%2B12%29+%29=0\".
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Look at \"-x%2Bhighlight_red%28+33+%29-4%2A%28-x%2B12%29=0\".
Moved \"33\" to the right of expression
It becomes \"-x-4%2A%28-x%2B12%29%2Bhighlight_green%28+33+%29=0\".
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Look at \"-x-highlight_red%28+4%2A%28-x%2B12%29+%29%2B33=0\".
Expanded term \"-4\" by using associative property on \"%28-x%2B12%29\"
It becomes \"-x%2Bhighlight_green%28+4%2Ax+%29-highlight_green%28+4%2A12+%29%2B33=0\".
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Look at \"-x%2B4%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+12+%29%2B33=0\".
Multiplied numerator integers
It becomes \"-x%2B4%2Ax-highlight_green%28+48+%29%2B33=0\".
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Look at \"-x%2B4%2Ax-highlight_red%28+48+%29%2Bhighlight_red%28+33+%29=0\".
Added fractions or integers together
It becomes \"-x%2B4%2Ax%2Bhighlight_green%28+-15+%29=0\".
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Look at \"-x%2B4%2Ax%2Bhighlight_red%28+-15+%29=0\".
Removed extra sign in front of \"-15\"
It becomes \"-x%2B4%2Ax-highlight_green%28+15+%29=0\".
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Look at \"-highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29-15=0\".
Eliminated similar terms \"highlight_red%28+-x+%29\",\"highlight_red%28+4%2Ax+%29\" replacing them with \"highlight_green%28+%28-1%2B4%29%2Ax+%29\"
It becomes \"highlight_green%28+%28-1%2B4%29%2Ax+%29-15=0\".
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Look at \"%28-highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2Ax-15=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+3+%29%29%2Ax-15=0\".
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Look at \"highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-15=0\".
Remove unneeded parentheses around factor \"highlight_red%28+3+%29\"
It becomes \"highlight_green%28+3+%29%2Ax-15=0\".
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Look at \"highlight_red%28+3%2Ax-15+%29=0\".
Solved linear equation \"highlight_red%28+3%2Ax-15=0+%29\" equivalent to 3*x-15 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=5.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=5, then 12-5=33-5=4*7 or 28=28 which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. ANSWER: Five years ago the father was 4 times as old as his son Paul.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful. \r
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\n" ); document.write( "\n" ); document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
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\n" ); document.write( "\n" ); document.write( "And good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
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\n" ); document.write( "\n" ); document.write( "drjctu@gmail.com\r
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