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| Math Central | Quandaries & Queries |
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Question from Lamarr, a student: A father is four times as old as his daughter is now. In 20 years he will be only twice as old as his daughter. How old are the father and daughter now? I cam e up with 40 years in 20years, putting the father at 20 years now and the daughter at 4 years of age. Is this correct and how do I write the problem up as a problem of solution |
Hi Lamarr,
If the daughter is 4 years old now and the father is 4 times as old as the daughter then the father would be 4 × 4 = 16 years old, so your answer can't be correct.
I would start by saying "Let the fathers age be f and the daughters age be d." The first clue says "A father is four times as old as his daughter is now." This translates to the equation
f = 4 × d
The second clue says "In 20 years he will be only twice as old as his daughter." In 20 years the father will be f + 20 years old and the daughter will be d + 20 years old. Translate the second clue into an equation.
Substitute the first equation, f = 4 × d, into the second equation and solve for d. Check your solution! does it satisfy both clues?
Penny
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