SOLUTION: A father told to his daughter, "when I was in your age, you were 4 years old, and when you are my age, I will be 88. What are their present ages?

Hi, there--

THE PROBLEM:
A father told to his daughter, "when I was in your age, you were 4 years old, and when you are my age, I will be 88. What are their present ages?

A SOLUTION:
Let F be the father's present age.
Let D be the daughter's present age.

Some number of years ago, say k years ago, the father was D years old, and the daughter was 
4 years old. So,
F - k = D
D - k = 4

Combine these equations to give,
F - D = D - 4
F - 2D = - 4

In some number of years, say m years, the father will be 88 hers old, and the daughter will be
F years old. So,
F + m = 88
D + m = F

Combine these equations to give,
F - D = 88 - F
2F - D = 88

Now we have two equations with two variables.
F - 2D = -4
2F - D = 88

Use the elimination method. Multiply each term in first equation by -2.
-2F + 4D = 8
  2F + -D = 88
-----------------
3D = 96
D = 32

The daughter is 32 years old. Substitute 32 for D in the first equation.

F - 2D = -4
F - 2(32) = -4
F = -4 + 64
F = 60

The father is 60 years old and the daughter is 32 years old.

Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com