When Katy was 12, her father was three times her age. Now he is twice her age. How old is Katy now?
Let Katy's age now = K
Let the Father's age now be F
Let x = the number of years ago it was when her father was 3 times her age.
When Katy was 12,
That was x years ago so
K - x = 12
her father was three times her age.
That was x years ago, so
F - x = 3(K - x)
Now he is twice her age
F = 2K
So we have this system of three equations:
K - x = 12
F - x = 3(K - x)
F = 2K
Simplifying them and putting the system in standard order
K - x = 12
-3K + F + 2x = 0
-2K + F = 0
Solve that by elimination or substitution and get
K=24, F=48, x=12
Answer: Katy is 24, her father is 48, (48 is twice her age 24, that checks)
12 years ago Katy was 12 and her father was 36 (36 is 3 times 12,
that checks).
Edwin
