Question 107157
Here's an easy method to these type of problems:
:
Write an equation for each statement:
:
A father is four times as old as his daughter is now.
F = 4D
:
"In 20 years," their age will be:
F+20
and
D+20
: 
In 20 years, he will be only twice as old as his daughter. 
F + 20 = 2(D+20)
F + 20 = 2D + 40
F = 2D + 40 - 20
F = 2D + 20
:
How old are the father and daughter now.
From the 1st statement: substitute 4D for F in the above equation:
4D = 2D + 20
4D - 2D = 20 
2D = 20
D = 20/2
D = 10 yrs old is the daughter now.
Then
4(10) = 40 yrs old is the father now
:
:
Check our solution using the statement:
"In 20 years, he will be only twice as old as his daughter."
(40 + 20) = 2(10 + 20); confirms out solution
:
Did this help you understand these type problems?