SOLUTION: Pam is half as old as her brother Bill. Four years ago Bill was six times older than Pam. How old is each sibling now?

Question 261051: Pam is half as old as her brother Bill. Four years ago Bill was six times older than Pam. How old is each sibling now?
Found 2 solutions by mananth, jsmallt9:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Pam is half as old as her brother Bill. Four years ago Bill was six times older than Pam. How old is each sibling now?
Let bills age be x
Pam�s age will be � *x
Four years ago
x-4
�*x-4
x-4 = 6*1/2*(x-4)
x-4 = 3x-12
-2x= -8
X=4
Bill�s age is 4 and Pam�s age is 2

M Ananth------------- mananth@hotmail.com

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(There is an error in another tutor's solution which caused his/her answer to be incorrect. The following is the same as the other solution up to the point of the error.)

Let x = Bill's age now.
Since Pam is half as old as Bill
= Pam's age now
Four years ago their ages would be four less than they are now:
x-4 = Bill's age four years ago
= Pam's age four years ago

Now that we have expressions for their ages now and four years ago, we can write an equation using the fact that four years ago Bill was six times as old as Pam:
[This is where the error was in the other solution.]
Using the Distributive Property on the right side we get:

This simplifies to:

Now we can solve for x. Subtract x from each side:

Add 24 to each side:

Divide both sides by 2:

Since x is Bill's age now, Bill is ten years old. And since Pam's age now is , Pam is five years old. (Four years ago Bill would be 6 and Pam would be 1 and Bill would have been 6 times as old. So our answers check.)
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