SOLUTION: Twice Mae's age added to Nora's age is 35. Five years ago, Nora was twice as old as Mae was then. Find the current age of each.

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Question 1170773: Twice Mae's age added to Nora's age is 35. Five years ago, Nora was twice as old as Mae was then. Find the current age of each.
Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%282m%2Bn=35%2Cn-5=2%28m-5%29%29
-
n-5=2m-10
2m-10-n=-5
2m-n=5


system%282m%2Bn=35%2C2m-n=5%29
4m=40
highlight%28m=10%29------------Mae currently
-
highlight%2815%29-------------Nora

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


It is good to take some time to analyze the problem to figure out the easiest way to solve the problem, rather than starting with direct translations of the given information into algebraic equations.

I think the following path to the answer is far easier (and faster) than the method shown by the other tutor -- primarily because it requires only a single variable and thus a single equation.

let x = Mae's age 5 years ago
then 2x = Nora's age 5 years ago

Then

x+5 = Mae's age now
2x+5 = Nora's age now

Twice Mae's age, added to Nora's age, is 35:

2%28x%2B5%29%2B%282x%2B5%29+=+35
2x%2B10%2B2x%2B5+=+35
4x%2B15+=+35
4x+=+20
x+=+5

ANSWERS:
Mae's current age is x+5=10
Nora's current age is 2x+5 = 15

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Twice Mae's age added to Nora's age is 35. Five years ago, Nora was twice as old as Mae was then. Find the current age of each.
Let Mae's age be M

Then, 2M + Nora's age = 35 ======> Nora = 35 - 2M

We then get: 35 - 2M - 5 = 2(M - 5)

                 30 - 2M = 2M - 10

               - 2M - 2M = - 10 - 30

                    - 4M = - 40

     Mae, or 

You can now find Nora's age!