A man is four times as old as his son . Five years ago, the man was seven times as old as his son
a. How old are they now
b. How old were they five years ago?
Let's represent the man's age as M and the son's age as S.
Given:
1) M = 4S (The man is four times as old as his son)
2) M - 5 = 7(S - 5) (Five years ago, the man was seven times as old as his son)
a) How old are they now?
Substituting equation 1) into equation 2) to eliminate M:
4S - 5 = 7(S - 5)
4S - 5 = 7S - 35
3S = 30
S = 10
Substituting S = 10 into equation 1) to find M:
M = 4(10)
M = 40
Therefore, the man is currently 40 years old, and the son is currently 10 years old.
b) How old were they five years ago?
The man's age five years ago would be M - 5 = 40 - 5 = 35.
The son's age five years ago would be S - 5 = 10 - 5 = 5.
Therefore, five years ago, the man was 35 years old, and the son was 5 years old.
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To solve this problem, we can set up a system of equations.
Let's assume the man's age is M and the son's age is S.
a. We know that "A man is four times as old as his son." So, we can write the equation: M = 4S.
b. We also know that "Five years ago, the man was seven times as old as his son." So, let's calculate their ages five years ago and set up another equation:
The man's age five years ago = M - 5
The son's age five years ago = S - 5
According to the second piece of information, "Five years ago, the man was seven times as old as his son," we can write the equation: M - 5 = 7(S - 5).
Now, we have two equations:
1. M = 4S (equation 1)
2. M - 5 = 7(S - 5) (equation 2)
To find the ages now (a) and the ages five years ago (b), we need to solve this system of equations.
a. Solving the system of equations:
Substitute equation 1 into equation 2:
4S - 5 = 7(S - 5)
Distribute the 7:
4S - 5 = 7S - 35
Combine like terms:
4S - 7S = -35 + 5
-3S = -30
S = -30 / -3
S = 10
Now, substitute the value of S back into equation 1 to find M:
M = 4(10)
M = 40
So, currently, the man is 40 years old, and the son is 10 years old.
b. To find their ages five years ago, subtract 5 from their current ages:
The man's age five years ago = 40 - 5 = 35 years old
The son's age five years ago = 10 - 5 = 5 years old
Therefore, five years ago, the man was 35 years old, and the son was 5 years old.