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 xx. The father's current age will then be 9x9x 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 x+3x + 3, and the father's age will be 9x+39x + 3. According to the problem, the father will then be 5 times the son's age:

9x+3=5(x+3)9x + 3 = 5(x + 3)

Step 2: Solve the equation

Expand and simplify:

9x+3=5x+159x + 3 = 5x + 15

Subtract 5x5x from both sides:

4x+3=154x + 3 = 15

Subtract 3 from both sides:

4x=124x = 12

Divide by 4:

x=3x = 3

Step 3: Find the father's age

The son's current age is x=3x = 3, so the father's current age is:

9x=9(3)=279x = 9(3) = 27

Thus, the father is 27 years old.


Would you like a detailed explanation of the steps?

Related Questions:

  1. What would be the son's age in 5 years?
  2. How can the problem be solved using a different approach, such as a system of equations?
  3. What if the father were 7 times the son's age? How would the solution change?
  4. What if the age difference between father and son were given instead of the ratio?
  5. 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