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A father's age is seven times that of his son's age. Three years from now, the age of the father will be five times that of his son's age. After how many years will their combined age be 62 years?
6 years
3 years
7 years
5 years
7 years
Use the ratio difference method: The gap between ratios (7:1 and 5:1) after 3 years is 2 units, which equals 3 years. Thus 1 unit = 1.5 years. Current ages: S=1.5├Ч1=1.5, F=1.5├Ч7=10.5. Required increase x for sum 62: (10.5+x)+(1.5+x)=62тЯ╣12+2x=62тЯ╣2x=50тЯ╣x=25. Wait, let me re-verify: 7S+3=5S+15тЯ╣2S=12тЯ╣S=6. So F=42. Now, 42+x+6+x=62тЯ╣48+2x=62тЯ╣2x=14тЯ╣x=7.
Father's age = 7 * Son's age. After 3 years, Father's age = 5 * (Son's age + 3). Combined age target = 62 years.
F=7S, F+3=5(S+3)
Use the ratio difference method: The gap between ratios (7:1 and 5:1) after 3 years is 2 units, which equals 3 years. Thus 1 unit = 1.5 years. Current ages: S=1.5├Ч1=1.5, F=1.5├Ч7=10.5. Required increase x for sum 62: (10.5+x)+(1.5+x)=62тЯ╣12+2x=62тЯ╣2x=50тЯ╣x=25. Wait, let me re-verify: 7S+3=5S+15тЯ╣2S=12тЯ╣S=6. So F=42. Now, 42+x+6+x=62тЯ╣48+2x=62тЯ╣2x=14тЯ╣x=7.
Confusing the 'After how many years' question with simply finding their current ages.
Define current ages
Let the son's present age be S. Then the father's present age is 7S.
F=7S
Use the future condition
After 3 years, the father's age will be 7S+3 and the son's will be S+3. According to the problem: 7S+3=5(S+3).
7S+3=5S+15
Solve for current ages
Simplifying the equation gives 2S=12, so S=6. The father's age is 7├Ч6=42.
S=6,F=42
Find years to reach combined age of 62
Let x be the number of years. The sum of their ages in x years will be (42+x)+(6+x)=62.
48+2x=62тЯ╣2x=14тЯ╣x=7
C is correct because calculating the current ages as 42 and 6, and adding x years to each to reach a sum of 62, results in x=7.
Age problems are essentially linear equations in one variable; always write the equation for both individuals at the specified time point.
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