SOLUTION: A man has two daughters, one three times as old as the other. The man is five times as old as his older daughter and in 5 years he will be five times as old as the younger. Find th
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Question 1120930: A man has two daughters, one three times as old as the other. The man is five times as old as his older daughter and in 5 years he will be five times as old as the younger. Find their present ages. Found 2 solutions by Boreal, greenestamps:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! older daughter is x years now. Man is 5x, younger daughter is 1/3 x.
In 5 years, man will be 5x+5 and younger daughter 1/3 x+5
so 5x+5=5((1/3 x +5)
5x+5=(5/3)x+25
(10/3)x=20, since 5x=15/3 x
10x=60
x=6 years older daughter
(1/3)x=2 years younger daughter
5x=30 years man.
In 5 years, he will be 35 and younger daughter 7, which is 5 times as much.
The solution by the other tutor is fine. However, I would define my variables differently to avoid having to work with fractions, since it's always more likely to make mistakes calculating with fractions than with whole numbers.
So let the younger daughter's age be x; then the older daughter's age is 3x; and then the father's age is 15x.
The father 5 years from now will be 5 times as old as his younger daughter:
The younger daughter is x=2; the older daughter is 3x=6; the father is 15x=30.
Note that, if a formal algebraic solution is not required, the problem can be solved quickly with a bit of logical reasoning.
Since the older daughter is 3 times as old as the younger daughter and the father is 5 times as old as his older daughter, the man is 15 times as old as his younger daughter.
Since ages (in age problems like this!) must be whole numbers, the possibilities for the ages of the younger daughter and the father are 1 and 15, or 2 and 30, or 3 and 45, or ....
Common sense tells us that 2 and 30 is by far the most likely combination; a bit of checking shows us that it satisfies all the conditions of the problem.
