Question 1120930
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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.<br>
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.<br>
The father 5 years from now will be 5 times as old as his younger daughter:<br>
{{{15x+5 = 5(x+5)}}}
{{{15x+5 = 5x+25}}}
{{{10x = 20}}}
{{{x = 2}}}<br>
The younger daughter is x=2; the older daughter is 3x=6; the father is 15x=30.<br>
Note that, if a formal algebraic solution is not required, the problem can be solved quickly with a bit of logical reasoning.<br>
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.<br>
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 ....<br>
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.