Age now problems

[Kendra]

A father is three times as old as the son, and the daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63
Find the present age of the father

 

[math_celebrity]

Let f be the age of the father and d be the age of the daughter and s be the age of the son. We have:

1. f = 3s
2. d = s - 3
3. d - 3 + f - 3 + s - 3 = 63

Simplify (3)
d + f + s - 9 = 63
d + f + s = 72

Now, substitute (1) and (2) into the modified (3)
(s - 3) + 3s + s = 72

Combine like terms:
5s - 3 = 72

Add 3 to each side
5s = 75

Divide each side by 5
s = 15

We want f, so we substitute s = 15 into (1)
f = 3(15)
f = 45