SOLUTION: Tom is half as old as Ellen was three years ago. In 10 years, Ellen will be one-and-one-half times as old as Tom. Would you please show me the formula to use? And the answer

Question 215999: Tom is half as old as Ellen was three years ago.
In 10 years, Ellen will be one-and-one-half times as old as Tom.
Would you please show me the formula to use? And the answer?
Thank you.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Tom is half as old as Ellen was three years ago.
In 10 years, Ellen will be one-and-one-half times as old as Tom.
Would you please show me the formula to use? And the answer?
I probably need more info but here is the problem set-up.

Step 1. Let be Tom's current age and let be Ellen's age

Step 2. Let be Tom's age three years ago and be Ellen's age three years ago

Step 3. Let be Ellen's age three years ago since Tom is half of Ellen's age three years ago. Simply this equation as follows

Add 6-y to both sides of the equation to isolate x and y terms on one side and numbers on the right side

Step 4. Let be Ellen's age in ten years since Ellen will be one and one half times as old as Tom where , x+10 is Tom's age in ten years, and y+10 is Ellen's age in ten years.

Multiply by 2 to both sides of the equation to get rid of denominator

Subtract 3x-20 to both sides of the equation

Step 5. Now we have a linear system of equations from Steps 3 and 4 and is shown below:

Step 6. Now solve the linear system of equations in Step 5 using substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
We'll use substitution. After moving -1*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=29. Since , x=16.

Answer: .

So x=16 and y=29.

Check the ages three ago

and where Ellen is twice the age of Tom three years ago...so this is a true statement.

Check the ages ten years from now.

and or which is another true statement.

Step 7. So Tom is 16 years old and Ellen is 29 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.

Good luck in your studies!

Respectfully,
Dr J

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