Question 814921
"My daughter is twice as old as my son. 
<pre>
D = 2S
</pre>
My wife is three times as old as the sum of the ages of my son and daughter,
<pre>
W = 3(S + D)
</pre>
and I am as old as my wife and my daughter. 
<pre>
We will let P = Mr. Parabola's age.

P = W + D
</pre>
My mother whose age is the total of all our ages is now 69."
<pre>
P + W + S + D = 69

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S we have a system of 4 equations and 4 unknown

D = 2S
W = 3(S + D)
P = W + D
69 = P + W + S + D

Substitute 2S for D in the other three

W = 3(S + 2S)
P = W + 2S
69 = P + W + S + 2S

Simplify
 
W = 3(3S)
P = W + 2S
69 = P + W + 3S

simplify more

W = 9S
P = W + 2S
69 = P + W + 3S

Substitute 9S for W in the other two
equations:

P = 9S + 2S
69 = P + 9S + 3S

Simplify

P = 11S
69 = P + 12S

Substitute 11S for P in the second equation

69 = 11S + 12S

Simplify

69 = 23S
 3 = S 

Substitute 3 for S in

69 = P + 12S
69 = P + 12(3)
69 = P + 36
33 = P

Substitute 3 for S in

W = 9S
W = 9(3)
W = 27

Substitute 3 for S in

D = 2S
D = 2(3)
D = 6

So the daughter is 6.

Edwin</pre>