SOLUTION: 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?

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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?
Found 2 solutions by scott8148, drj:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"Four years ago, Katie was twice as old as Anne was then" ___ K - 4 = 2(A - 4) ___ K - 4 = 2A - 8

"In 6 years, Anne will be the same age that Katie is now" ___ A + 6 = K

substituting ___ (A + 6) - 4 = 2A - 8 ___ 10 = A

substituting ___ (10) + 6 = K ___ 16 = K

Answer by drj(1380) About Me  (Show Source):
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?

Step 1. Let x be the age of Anne

Step 2. Let x-4 be the age of Anne four years ago.

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

Step 4. Let x+6 be the Age of Anne in six years.

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.
Step 6. Then, x+6=2(x-4)+4 since in 6 years Anne will be the same age that Katie is now.

Step 7. Solving yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • 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.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
This is an equation! Solutions: x=10.

Universal Simplifier and Solver


Done!



With x=10, then 2(x-4)+4=16

Step 8 ANSWER. Anne is 10 years old and Katie is 16 years old.

I hope the above steps were helpful.

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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV