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In a family, the sum of the ages of a father and son is 50 years. 10 years from now, the difference in their ages will be 20 years. Find the ratio of the son's age to the father's age.
7
7
5:8
7
7
The difference in ages always remains constant. If the difference is 20, then FтИТS=20. Since F+S=50, solving this system yields F=35 and S=15. The ratio is 15:35, which simplifies to 3:7.
Sum of father's age (F) and son's age (S) is 50. The difference between their ages 10 years later is 20.
F+S=50 and FтИТS=20
The difference in ages always remains constant. If the difference is 20, then FтИТS=20. Since F+S=50, solving this system yields F=35 and S=15. The ratio is 15:35, which simplifies to 3:7.
Students often wrongly calculate the difference after 10 years as (F+10) - (S+10) + 20, failing to realize that adding 10 to both ages does not change the age difference.
Define Equations
Let Father's age be F and Son's age be S. Based on the problem, the sum is 50, and the difference is 20.
F+S=50, FтИТS=20
Solve for F and S
Add the two equations to eliminate S: (F+S)+(FтИТS)=50+20, which gives 2F=70.
F=35
Find Son's Age
Substitute F=35 into F+S=50 to find S.
S=50тИТ35=15
Calculate Ratio
Find the ratio of son's age to father's age: S:F=15:35. Simplify by dividing by 5.
3515тАЛ=73тАЛ
A is correct because the father's age is 35 and the son's age is 15, resulting in a ratio of 15:35, which simplifies to 3:7.
In age-related problems, always remember that the 'difference in ages' is an invariant quantity regardless of how many years pass in the future or past.
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