Mother's Age in Terms of Daughter's

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

The sum of the ages of a father, a mother, and a daughter is 73. When 
the father is twice as old as the daughter, the sum of their two ages 
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.

Give it a try and if you want to check your solution with me, write 
back. If you are having difficulties, let me know and show me what you 
have done so far, and I'll try to help you some more.

Good luck.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/