Math Problem Statement
a father is 9 times the age of his son . 3 years from now the father will be only 5 times asold as his son then . what is the age of the father now ?
Solution
Let the son's current age be . The father's current age will then be since he is 9 times older than his son.
Step 1: Set up the equation based on the future ages
In 3 years, the son's age will be , and the father's age will be . According to the problem, the father will then be 5 times the son's age:
Step 2: Solve the equation
Expand and simplify:
Subtract from both sides:
Subtract 3 from both sides:
Divide by 4:
Step 3: Find the father's age
The son's current age is , so the father's current age is:
Thus, the father is 27 years old.
Would you like a detailed explanation of the steps?
Related Questions:
- What would be the son's age in 5 years?
- How can the problem be solved using a different approach, such as a system of equations?
- What if the father were 7 times the son's age? How would the solution change?
- What if the age difference between father and son were given instead of the ratio?
- How would this problem change if we worked in months instead of years?
Tip: Always check your solution by substituting the values back into the original conditions!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Age relation formula: Future age = Current age + Time elapsed
Theorems
Linear equation principles for solving single-variable equations
Suitable Grade Level
Grades 6-8