A man is 4 times as old as his son. In 20 years, the man will be twice as old as

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Question: A man is 4 times as old as his son. In 20 years, the man will be twice as old as his son. What is the current age of the son?

Options:

Correct Answer: 10 years

Solution:

Let the son\'s age be x. Then the man\'s age is 4x. In 20 years, 4x + 20 = 2(x + 20). Solving gives x = 10.

A man is 4 times as old as his son. In 20 years, the man will be twice as old as his son. What is the current age of the son?

A man is 4 times as old as his son. In 20 years, the man will be twice as old as his son. What is the current age of the son?

Step 1: Let the son's current age be represented by 'x'.
Step 2: Since the man is 4 times as old as his son, we can express the man's age as '4x'.
Step 3: In 20 years, the son's age will be 'x + 20'.
Step 4: In 20 years, the man's age will be '4x + 20'.
Step 5: According to the problem, in 20 years, the man will be twice as old as his son. We can write this as the equation: '4x + 20 = 2(x + 20)'.
Step 6: Now, simplify the equation: '4x + 20 = 2x + 40'.
Step 7: Subtract '2x' from both sides: '4x - 2x + 20 = 40'.
Step 8: This simplifies to '2x + 20 = 40'.
Step 9: Now, subtract 20 from both sides: '2x = 20'.
Step 10: Finally, divide both sides by 2 to find 'x': 'x = 10'.

Algebraic Equations – The problem involves setting up and solving linear equations based on relationships between ages.
Age Relationships – Understanding how to express age relationships and changes over time.