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?

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) (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) (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 was fully solved.
Text form: x+6=2*(x-4)+4 simplifies to 0=0
Cartoon (animation) form:
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 .
Moved these terms to the left ,
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Removed extra sign in front of
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Remove extraneous '1' from product
It becomes .

Look at .
Solved linear equation equivalent to -x+10 =0
It becomes .
Result:
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

RELATED QUESTIONS
Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be the... (answered by edjones,stanbon)
four years ago, katie was twice as old as anne was then. in 6 years, anne will be the... (answered by stanbon)
Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be the... (answered by College Student)
Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be the... (answered by ankor@dixie-net.com)
Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be the... (answered by dabanfield)
Four years ago Katie was twice as old as Anne was then. in 6 years, Anne will be the same (answered by drj)
1. Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be... (answered by ankor@dixie-net.com)
4 years ago katie was twice as old as anne was. In 6 years ann will be the same age that (answered by macston)
how whould i set up an equation for this word problem four years ago, katie was twice... (answered by solver91311)