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Mother's Age in Terms of Daughter's

Date: 06/27/2001 at 14:08:00
From: claudia garcia
Subject: Some type of algebra

will be 132. Write an equation expressing the mother's present 
age in terms of the daughter's present age.

I have done several things but I am not sure about the answer. Here is 
what I have done. Could you tell me if it's right, and if not, could 
you help??

a. f + m + d = 132
b. 2d + f = 132

2. Next I subtracted the two equations to cancel out the father and 
get the mother in terms of the daughter.

-f-m-d = -73 (multiplied the top by -1)
+f -2d = 132 

3. Solve 

-m-3d = 59
isolate the m, so m = -3d + 59

Date: 06/27/2001 at 15:18:06
From: Doctor Jaffee
Subject: Re: Some type of algebra

Hi Claudia,

The mistake you made was in the equation 2d + f = 132, which can be 
translated as "The daughter's current age doubled plus the father's 
current age equals 132."

Look at it it this way. In x years the father will be f + x years old, 
and in x years the daughter will be d + x years old. At that time the 
father will be twice as old as the daughter, so f + x = 2(d + x).

Solving for x we get x = f - 2d.

So the father's age is now f + x = f + (f - 2d) = 2f - 2d
 and the daughter's age is d + x = d + f - 2d = f - d.

Therefore, the sum of their ages at this time is 3f - 3d = 132.

You should be able to work it from here and find that there are a 
number of plausible solutions, although in each case, the father is 
old enough to be his wife's father.


Good luck.

- Doctor Jaffee, The Math Forum
Associated Topics:
High School Basic Algebra
Middle School Algebra
Middle School Word Problems

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