Three years ago the sum of the ages of the father and son was 48 years...
SOLUTION :
Let the current ages of the father be F and that of the son, S.
Three years ago their ages were (F-3) and (S-3) and the sum was 48, or
Equate (1) and (2): 54-S = 3S+6, or
4S=48, or S = 12 and So F = 42.
The father is 42 years and the son 12 years, now.
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Three years ago the sum of the ages of the father and son was 48 years...
Given:
Three years ago, the sum of the ages of the father and son was 48 years.
After 3 years, the ratio of the father's age to the son's age will be 3:1.
To find:
How much older is the father from the son?
Solution:
Let's assume the present age of the father as F years and the present age of the son as S years.
Step 1:
Three years ago, the father's age was F-3 and the son's age was S-3.
According to the given information, the sum of their ages three years ago was 48 years.
So, we can write the equation:
(F-3) + (S-3) = 48
Simplifying the equation, we get:
F + S - 6 = 48
F + S = 48 + 6
F + S = 54
Step 2:
After 3 years, the father's age will be F+3 and the son's age will be S+3.
According to the given information, the ratio of their ages after 3 years will be 3:1.
So, we can write the equation:
(F+3) : (S+3) = 3 : 1
Cross-multiplying, we get:
(F+3) * 1 = (S+3) * 3
F + 3 = 3S + 9
F = 3S + 9 - 3
F = 3S + 6
Step 3:
Now, we have two equations:
F + S = 54 (from Step 1)
F = 3S + 6 (from Step 2)
Substituting the value of F from Step 2 into the first equation, we get:
(3S + 6) + S = 54
4S + 6 = 54
4S = 54 - 6
4S = 48
S = 48/4
S = 12
Step 4:
Substituting the value of S into the equation F = 3S + 6, we get:
F = 3(12) + 6
F = 36 + 6
F = 42
Step 5:
Now that we know the present ages of the father and son, we can find out how much older the father is from the son.
The father's age is 42 and the son's age is 12.
So, the father is 42 - 12 = 30 years older than the son.
Therefore, the father is 30 years older than the son.
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