document.write( "Question 227678: Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be the same age that Katie is now. How old is each? \n" ); document.write( "

Algebra.Com's Answer #169150 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be the same age that Katie is now. How old is each?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let x be the age of Anne\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let x-4 be the age of Anne four years ago.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 2(x-4) be the age of Katie four years ago and Katie is also twice as old as Anne four years ago\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let x+6 be the Age of Anne in six years.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Let 2(x-4)+4 be the age of Katie NOW where we added 4 years to the equation found in Step 3.\r
\n" ); document.write( "\n" ); document.write( "Step 6. Then, x+6=2(x-4)+4 since in 6 years Anne will be the same age that Katie is now.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. Solving yields the following steps:\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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This is an equation! Solutions: x=10.
Graphical form: Equation $\"x%2B6=2%2A%28x-4%29%2B4\"$ was fully solved.
Text form: x+6=2*(x-4)+4 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+x%2B6=2%2A%28x-4%29%2B4+%29\"$
For tutors: simplify_cartoon( x+6=2*(x-4)+4 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"x%2B6=highlight_red%28+2%2A%28x-4%29%2B4+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2%2A%28x-4%29+%29\"$ , $\"highlight_green%28+-4+%29\"$
It becomes $\"x%2B6-highlight_green%28+2%2A%28x-4%29+%29-highlight_green%28+4+%29=0\"$ .
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Look at $\"x%2Bhighlight_red%28+6+%29-2%2A%28x-4%29-highlight_red%28+4+%29=0\"$ .
Added fractions or integers together
It becomes $\"x%2Bhighlight_green%28+2+%29-2%2A%28x-4%29=0\"$ .
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Look at $\"x%2Bhighlight_red%28+2+%29-2%2A%28x-4%29=0\"$ .
Moved $\"2\"$ to the right of expression
It becomes $\"x-2%2A%28x-4%29%2Bhighlight_green%28+2+%29=0\"$ .
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Look at $\"x-highlight_red%28+2%2A%28x-4%29+%29%2B2=0\"$ .
Expanded term $\"-2\"$ by using associative property on $\"%28x-4%29\"$
It becomes $\"x-highlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A4+%29%2B2=0\"$ .
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Look at $\"x-2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+4+%29%2B2=0\"$ .
Multiplied numerator integers
It becomes $\"x-2%2Ax%2Bhighlight_green%28+8+%29%2B2=0\"$ .
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Look at $\"x-2%2Ax%2Bhighlight_red%28+8+%29%2Bhighlight_red%28+2+%29=0\"$ .
Added fractions or integers together
It becomes $\"x-2%2Ax%2Bhighlight_green%28+10+%29=0\"$ .
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Look at $\"highlight_red%28+x+%29-highlight_red%28+2%2Ax+%29%2B10=0\"$ .
Eliminated similar terms $\"highlight_red%28+x+%29\"$ , $\"highlight_red%28+-2%2Ax+%29\"$ replacing them with $\"highlight_green%28+%281-2%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%281-2%29%2Ax+%29%2B10=0\"$ .
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Look at $\"%28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2Ax%2B10=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-1+%29%29%2Ax%2B10=0\"$ .
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Look at $\"%28highlight_red%28+-1+%29%29%2Ax%2B10=0\"$ .
Removed extra sign in front of $\"-1\"$
It becomes $\"%28-highlight_green%28+1+%29%29%2Ax%2B10=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+1+%29%29%2Ax+%29%2B10=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$
It becomes $\"-highlight_green%28+1+%29%2Ax%2B10=0\"$ .
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Look at $\"-highlight_red%28+1+%29%2Ax%2B10=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"-x%2B10=0\"$ .
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Look at $\"highlight_red%28+-x%2B10+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-x%2B10=0+%29\"$ equivalent to -x+10 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=10.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With x=10, then 2(x-4)+4=16\r
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\n" ); document.write( "\n" ); document.write( "Step 8 ANSWER. Anne is 10 years old and Katie is 16 years old.\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 in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and 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
\n" ); document.write( "\n" ); document.write( "http://www.FreedomUniversity.TV\r
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