A father is 4 times as old as his son. If the sum of their ages is 50 years, how

A father is 4 times as old as his son. If the sum of their ages is 50 years, how old is the father?

A father is 4 times as old as his son. If the sum of their ages is 50 years, how old is the father?

Correct Answer: 40

Step 1: Let the son's age be represented by the variable x.
Step 2: Since the father is 4 times as old as the son, we can represent the father's age as 4x.
Step 3: The problem states that the sum of their ages is 50 years. We can write this as an equation: x + 4x = 50.
Step 4: Combine the terms on the left side of the equation: 5x = 50.
Step 5: To find the value of x (the son's age), divide both sides of the equation by 5: x = 50 / 5.
Step 6: Calculate the value: x = 10. This means the son is 10 years old.
Step 7: Now, to find the father's age, substitute x back into the father's age equation: Father's age = 4x = 4 * 10.
Step 8: Calculate the father's age: Father's age = 40.

Algebraic Equations – The question tests the ability to set up and solve linear equations based on relationships between variables.
Age Problems – It specifically focuses on age-related problems, which often involve ratios and sums of ages.