Question 157569
The ages of Paul and Judy total 27 years
Judy's age plus twice Paul' age is 43 
First translate the words into an algebra equation
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Use P for Paul's age and J for Judy's age.  It saves typing.
The 1st sentence says P + J = 27.  So far so good.
Then the 2nd sentence:
J + 2*P = 43  See that?  
Now we have 2 eqns in 2 unknowns, so we can solve for P and J (not PB & J, tho)
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J + P = 27    EQN 1
J + 2P = 43   EQN 2
Subtract EQN 1 from EQN 2
0 + P = 16
So Paul is 16
27 - 16 = 11, so 
Jane is 11.

That's it.