Math Problem Statement
A father is five times as old as his son. In 27 years’ time he will be twice as old as his son. Find their present ages.
Solution
Let the present age of the son be .
Since the father is five times as old as the son, the present age of the father is .
In 27 years, the son's age will be , and the father's age will be .
According to the problem, in 27 years, the father will be twice as old as the son. Therefore, we can set up the following equation:
Solving the equation:
- Expand both sides:
- Subtract from both sides:
- Subtract 27 from both sides:
- Divide by 3:
So, the son's present age is 9 years.
Now, to find the father's age:
Conclusion:
- The son's present age is 9 years.
- The father's present age is 45 years.
Would you like any further details or have any questions about this solution? Here are some related questions:
- What would the ages of the son and father be in 10 years?
- How would the solution change if the father was 3 times as old as the son instead of 5 times?
- If the son was 12 years old, how old would the father be if the same relationship holds?
- How can you set up an equation for situations like this where the future relationship between ages is known?
- What other types of age-related word problems can be modeled using algebra?
Tip: When dealing with age problems, let variables represent the unknowns (like the son's age), and use the relationships described to set up equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Age Problems
Formulas
x + 27
5x + 27 = 2(x + 27)
Theorems
Solving linear equations
Substitution method
Suitable Grade Level
Grades 6-8