SOLUTION: Archie is 6 years older than Betty. In two years, Archie will be twice as old as Betty. How old is Betty?

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Question 1174900: Archie is 6 years older than Betty. In two years, Archie will be twice as old as Betty. How old is Betty?
Found 4 solutions by math_tutor2020, ewatrrr, greenestamps, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Edit: Made a brainfart of a typo, but it has been fixed.

A = Archie's age right now
B = Betty's age right now
A and B are some positive whole number.

A = B+6 since Archie is 6 years older than Betty (I'm assuming at this current time)

In 2 years, Archie will be A+2 years old and Betty will be B+2 years old

Since in this future date, he is twice as old as Betty's age, this means
A+2 = 2*(B+2)

We can plug in A = B+6 and solve for B
A+2 = 2*(B+2)
B+6+2 = 2*(B+2)
B+8 = 2*(B+2)
B+8 = 2B+4
B-2B = 4-8
-B = -4
B = 4

Betty is currently 4 years old.
Archie is A = B+6 = 4+6 = 10 years old currently.

In 2 years, we have these future ages
Archie: A+2 = 10+2 = 12
Betty: B+2 = 4+2 = 6

Two years into the future, Archie's future age (12) is exactly twice that of Betty's future age (6). This helps us confirm the answer.

Answer: Betty is currently 4 years old.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
(Archie is 6 years older than Betty) 'x'
In two years...
 (x+6) +2 = 2(x+2) 
   x + 8 = 2x + 4
       4 = x, Betty's age NOW 
In two years...
 12 = 2(6)  checks

Wish You the Best in your Studies.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


You have responses showing good formal algebraic solutions, using standard algebraic techniques. One solution uses a single variable; the other uses two. That is good; you should know both methods for solving the problem.

If a formal algebraic solution is not required, you can get some good mental exercise (more than by following formal algebraic steps) by solving the problem informally, using logical reasoning and simple mental arithmetic.

Archie is 6 years older than Betty. (Now; and always).
So when Archie is twice as old as Betty, their ages will be 12 and 6.
Since that will be 2 years from now, their current ages are 10 and 4.

ANSWER: Betty is (now) 4 years old.
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
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Archie is 6 years older than Betty. In two years, Archie will be twice as old as Betty.
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