Question 935064
<pre>
Let:
F = father's age
M = mother's age
S = son's age
D = each of the twin daughter's age
</pre>
>>Our family of two adults and three children is exactly 123 years<< 
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F+M+S+2D = 123
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>>The father and son’s ages, when added are 59,<<
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F+S = 59
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which [59] is 5 years less than the mother and the twin girls.
<pre>
59 = M+2D-5
64 = M+2D
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>>The father is three years older than the mother,<<
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F = M+3
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>>the son is three years older than the girls.<<
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S = D+3 

So we have this system of 5 equations in 4 unknowns.
That means we were given more information that we needed.

{{{system(F+M+S+2D=123, F+S=59, 64=M+2D, F=M+3, S=D+3)}}}

Substitute D+3 for S in the first 4 equations and simplify:

{{{system(F+M+3D+2D=120, F+D=56, 64=M+2D, F=M+3)}}}

Substitute M+3 for F in the first 3 equations and simplify:

{{{system(2M+5D=117, M+D=53, 64=M+2D)}}}

Solve the middle equation for M:  M=53-D. Substitute in the
other 2 equations:

{{{system(2(53-D)+5D=117, 64=53-D+2D)}}}

{{{system(D=11, 11=D)}}}

So the twin daughters are 11 each.

M=53-D = 53-11 = 42, so the mother is 42.

F=M+3 = 42+3 = 45, so the father is 45.

S=D+3 = 11+3 = 14, so the son is 14.

Edwin</pre>