SOLUTION: Paula is 12 years older than her brother Bob. Four years from now Bob wil be two thirds as old as Paula. How old are they now?

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Question 227956: Paula is 12 years older than her brother Bob. Four years from now Bob wil be two thirds as old as Paula. How old are they now?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Paula is 12 years older than her brother Bob. Four years from now Bob will be two thirds as old as Paula. How old are they now?

Step 1. Let x be the age of Bob

Step 2. Let x+12 be the age of Paula since she's 12 years older than Bob.

Step 3. Let x+4 be the age of Bob in four years.

Step 4. Let x+12+4=x+16 be the age of Paula in four years.

Step 5. Then, x%2B4=2%28x%2B16%29%2F3 since in four years from now Bob will be two thirds as old as Paula.

Step 6. Solving the equation in Step 5 x%2B4=2%28x%2B16%29%2F3 yields the following steps

Multiply by 3 to both sides of the equation to get rid of the denominator.

3%28x%2B4%29=3%2A%282%28x%2B16%29%2F3%29

3x%2B12=2x%2B32

Subtract 2x+12 from both sides of the equation

3x%2B12-%282x%2B12%29=2x%2B32-%282x%2B12%29

x=20 and x%2B12=32

Check the solution x=3 and substitute into original equation x%2B4=2%28x%2B16%29%2F3

20%2B4=2%2820%2B16%29%2F3

24=2%2836%29%2F3

24=24 which is a true statement.

Step 7. ANSWER: Bob is 20 years old and Paula is 32 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