If a mother is 6 times as old as her daughter now, and in 6 years, she will be 4 times as old as her daughter, how old is the daughter now?
Practice Questions
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If a mother is 6 times as old as her daughter now, and in 6 years, she will be 4 times as old as her daughter, how old is the daughter now?
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Let the daughter's age be x. Then the mother's age is 6x. In 6 years, the mother will be 6x + 6 and the daughter will be x + 6. The equation is 6x + 6 = 4(x + 6), which simplifies to 6x + 6 = 4x + 24, so 2x = 18, and x = 9.
Questions & Step-by-step Solutions
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Q
Q: If a mother is 6 times as old as her daughter now, and in 6 years, she will be 4 times as old as her daughter, how old is the daughter now?
Solution: Let the daughter's age be x. Then the mother's age is 6x. In 6 years, the mother will be 6x + 6 and the daughter will be x + 6. The equation is 6x + 6 = 4(x + 6), which simplifies to 6x + 6 = 4x + 24, so 2x = 18, and x = 9.
Steps: 12
Step 1: Let the daughter's current age be represented by 'x'.
Step 2: Since the mother is 6 times as old as her daughter, her current age is '6x'.
Step 3: In 6 years, the daughter's age will be 'x + 6'.
Step 4: In 6 years, the mother's age will be '6x + 6'.
Step 5: According to the problem, in 6 years, the mother will be 4 times as old as the daughter. This gives us the equation: '6x + 6 = 4(x + 6)'.
Step 6: Expand the right side of the equation: '6x + 6 = 4x + 24'.
Step 7: To solve for 'x', first subtract '4x' from both sides: '6x - 4x + 6 = 24'.
Step 8: This simplifies to '2x + 6 = 24'.
Step 9: Next, subtract 6 from both sides: '2x = 24 - 6'.
Step 10: This simplifies to '2x = 18'.
Step 11: Finally, divide both sides by 2 to find 'x': 'x = 18 / 2'.
Step 12: Therefore, 'x = 9', which means the daughter is currently 9 years old.
