Question 1204835
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A typical formal algebraic solution would start with the given information that the sum of the man's age and his daughter's age is 120:<br>
m = man's age
d = daughter's age
m+d=120<br>
Then the next step would be to write the equation that says six years ago the man was three times as old as his daughter:<br>
m-6 = man's age 6 years ago
d-6 = daughter's age 6 years ago
m-6=3(d-6)<br>
From there some method would be used to solve the system of two equations in m and d to find their current ages.<br>
I leave it to you to follow through with that solution method if you want; it is good algebra practice.<br>
But a different setup for solving the problem, using a single variable, makes solving the problem easier.<br>
Instead of starting with the first piece of given information, start with the second.  6 years ago, the man was three times as old as his daughter:<br>
x = daughter's age 6 years ago
3x = man's age 6 years ago<br>
The sum of their ages now is 120:<br>
x+6 = daughter's age now
3x+6 = man's age now
{{{(x+6)+(3x+6)=120}}}
{{{4x+12=120}}}
{{{4x=108}}}
{{{x=27}}}<br>
ANSWERS: Their ages now are
daughter: x+6 = 27+6 = 33
man: 3x+6 = 81+6 = 87<br>