A mother is 4 times as old as her daughter. After 8 years, the mother will be tw

A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. How old is the daughter now?

A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. How old is the daughter now?

Correct Answer: 8

Step 1: Let the daughter's current age be represented by 'x'.
Step 2: Since the mother is 4 times as old as her daughter, we can express the mother's age as '4x'.
Step 3: In 8 years, the daughter's age will be 'x + 8'.
Step 4: In 8 years, the mother's age will be '4x + 8'.
Step 5: According to the problem, in 8 years, the mother will be twice as old as the daughter. We can write this as the equation: '4x + 8 = 2(x + 8)'.
Step 6: Now, simplify the equation: '4x + 8 = 2x + 16'.
Step 7: Subtract '2x' from both sides: '4x - 2x + 8 = 16'.
Step 8: This simplifies to '2x + 8 = 16'.
Step 9: Now, subtract 8 from both sides: '2x = 16 - 8'.
Step 10: This simplifies to '2x = 8'.
Step 11: Finally, divide both sides by 2 to find 'x': 'x = 8'.
Step 12: Therefore, the daughter's current age is 8 years.

Algebraic Equations – The question tests the ability to set up and solve linear equations based on relationships between ages.
Age Problems – It involves understanding how to manipulate age-related problems over time.