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In 1918 his father's age was 9 times his son's age; In 1923 the father's age was five times that of his son. What was the father's age in 1940?

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Answer to a math question In 1918 his father's age was 9 times his son's age; In 1923 the father's age was five times that of his son. What was the father's age in 1940?

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Esmeralda
4.7
101 Answers
Let's let the present age of the father be represented by F, and the present age of the son be represented by S.

Step 1: Translate the given information into equations:
In 1918 (F-22) = 9(S-22) - we subtract 22 from both the father's and son's age to find their ages back in 1918.
In 1923 (F-17) = 5(S-17) - we subtract 17 from both the father's and son's age to find their ages back in 1923.

Step 2: Simplify the equations:
F - 22 = 9S - 198
F - 17 = 5S - 85

Step 3: Solve the system of equations:
Using the second equation, we can express F in terms of S:
F = 5S - 68

Substituting this expression for F into the first equation, we can solve for S:
5S - 68 - 22 = 9S - 198
5S - 90 = 9S - 198
4S = 108
S = 27

Step 4: Find the father's age in 1940:
To find the father's age in 1940, we need to add 22 years to the son's age in 1940 and substitute it into the expression for F:
F = 5(27) - 68
F = 135 - 68
F = 67

Answer:
The father's age in 1940 was 67.

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