SOLUTION: Betty's present age is twice Roni's present age. Two years ago, Betty was three times as old as Roni was then. Find their present ages.

Question 118137: Betty's present age is twice Roni's present age. Two years ago, Betty was three times as old as Roni was then. Find their present ages.
Found 2 solutions by bucky, Nate:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let B represent Betty's present age and R represent Roni's present age.
.
The problem tells you that Betty's present age is 2 times Roni's present age. In equation form
this is:
.
B = 2R
.
Two years ago how old was Betty? Take Betty's present age B and subtract 2 to get B - 2. And
two years ago how old was Roni? Take Roni's present age R and subtract 2 to get R - 2. The problem
then tells you that Betty's age 2 years ago (B - 2) was three times Roni's age at that time
or ... 3 times (R - 2). In equation form this is:
.
B - 2 = 3(R - 2)
.
Multiply out the right side by multiplying 3 times each of the terms in the parentheses, and
when you do that multiplication, the equation becomes:
.
B - 2 = 3R - 6
.
Get rid of the -2 on the left side by adding +2 to both sides. That addition makes the
equation become:
.
B = 3R - 4
.
Next, get rid of the 3R on the right side by subtracting 3R from both sides to change the
equation to:
.
B - 3R = -4
.
Recall that the very first equation above told you that B equaled 2R. So you can substitute
2R for B in the equation directly above to change it to:
.
2R - 3R = -4
.
Combining the two terms on the left side leads to:
.
-R = -4
.
Multiply both sides of this equation by -1 and you end up with:
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R = 4
.
So Roni's present age (R) is 4 years old. And since Betty's present age is equal to 2 times R,
then Betty is presently 2 times 4 or 8 years old.
.
Check. Two years ago Betty would have been 8 - 2 or 6 years old and Roni would have been
4 - 2 or 2 years old. And at that time Betty's age (6) was actually 3 times Roni's age (2).
So the answers check ... Betty is now 8 and Roni is now 4.
.
Hope this helps you to understand the problem and how to do it.
.
Happy 2008!!!!
.
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Roni's = x
Betty's age = 2x
~~~~
Roni's = x - 2
Betty's age = 3(x - 2) = 3x - 6
~~~~
2x - 2 = 3x - 6
-2 = x - 6
4 = x
~~~~
Roni's = x = 4 years
Betty's age = 2x = 8 years
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