Ten years ago a man was three times as old as his son. In twelve more years, the son is three-fifths as old as his father. What were their ages 5 years ago?
if the man is now m and the son s,
m-10 = 3(s-10)
(3/5)(m+12) = s+12
m-5 = 38
s-5 = 16
To solve this problem, we can first assign variables to the ages of the man and his son. Let's say the man's age is M and the son's age is S.
According to the given information, "Ten years ago, a man was three times as old as his son." So, we can set up the equation:
M - 10 = 3(S - 10) .....(1)
Next, we are given that "in twelve more years, the son is three-fifths as old as his father." This gives us another equation:
S + 12 = (3/5)(M + 12) .....(2)
Now, let's solve these two equations simultaneously to find the values of M and S.
To solve equation (1):
Distribute 3 to (S - 10):
M - 10 = 3S - 30
M = 3S - 20 .....(3)
Substituting equation (3) into equation (2):
S + 12 = (3/5)((3S - 20) + 12)
S + 12 = (3/5)(3S - 8)
S + 12 = (9/5)S - 24/5
Multiply through by 5 to get rid of the fraction:
5S + 60 = 9S - 24
5S - 9S = -24 - 60
-4S = -84
S = -84 / -4
S = 21
Substituting the value of S into equation (3):
M = 3S - 20
M = 3(21) - 20
M = 63 - 20
M = 43
Therefore, currently, the man is 43 years old and his son is 21 years old.
To find their ages 5 years ago, simply subtract 5 from each of their ages:
Man's age 5 years ago = 43 - 5 = 38
Son's age 5 years ago = 21 - 5 = 16
So, their ages 5 years ago were 38 and 16, respectively.