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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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?
Esmeralda
4.7102 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.
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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