SOLUTION: The sum of age's of a man and his daughter is 120years.six years ago,the man's age was thrice that of his daughter.find their present age.

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Question 1204835: The sum of age's of a man and his daughter is 120years.six years ago,the man's age was thrice that of his daughter.find their present age.
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52786) About Me  (Show Source):
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.
The sum of age's of a man and his daughter is 120years.
six years ago,the man's age was thrice that of his daughter.find their present age.
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Let x be the daughter's age, in years.

Then the the father's age is (120-x) years.


Six years ago

    ((120-x)-6) = 3*(x-6).


Simplify and find x

    114-x = 3x - 18

    114 + 18 = 3x + x

    132 = 4x

    132/4 = x

    x = 33.


The daughter's current age is 33 years.

The father's current age is 120-33 = 87 years.

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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:

m = man's age
d = daughter's age
m+d=120

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:

m-6 = man's age 6 years ago
d-6 = daughter's age 6 years ago
m-6=3(d-6)

From there some method would be used to solve the system of two equations in m and d to find their current ages.

I leave it to you to follow through with that solution method if you want; it is good algebra practice.

But a different setup for solving the problem, using a single variable, makes solving the problem easier.

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:

x = daughter's age 6 years ago
3x = man's age 6 years ago

The sum of their ages now is 120:

x+6 = daughter's age now
3x+6 = man's age now
%28x%2B6%29%2B%283x%2B6%29=120
4x%2B12=120
4x=108
x=27

ANSWERS: Their ages now are
daughter: x+6 = 27+6 = 33
man: 3x+6 = 81+6 = 87

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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The sum of age's of a man and his daughter is 120years.six years ago,the man's age was thrice that of his daughter.
find their present age.
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The sum of age's of a man and his daughter is T years. v years ago, the man's age was k times that of his daughter.
find their present age.
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Man, y
Daughter,T-y

highlight_green%28y-v=k%28T-y-v%29%29, with only y, as the unknown variable (the man's age).

y-v=kT-ky-kv
y%2Bky=v%2BkT-kv
y%281%2Bk%29=v%2BkT-kv
highlight_green%28y=%28v%2BkT-kv%29%2F%28k%2B1%29%29

The description gave
T=120
v=6
k=3
y is solved; only need to substitute the given values.
y=%286%2B3%2A120-3%2A6%29%2F%283%2B1%29
y=%286%2B360-18%29%2F4
y=%28360-12%29%2F4=90-3
highlight%28y=87%29-----------the man
T-y=highlight%2833%29---------daughter