Question 1020094
.
If Peter’s age + Paul’s age = 39
and Peter’s age + Mary’s age = 44

and Paul’s age + Mary’s age = 47

how old are Peter, Paul and Mary?
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<pre>
Peter + Paul = 39,     (1)
Peter + Mary = 44,     (2)
Paul  + Mary = 47.     (3)

Add all three equations (1), (2) and (3) (both sides). You will get

2(Peter + Paul + Mary) = 130,   or

Peter + Paul + Mary = 65.    (4)

Now distract equation (1) from (4). You will get

Mary's age = 65 - 39 = 26.

Next, distract equation (2) from (4). You will get

Paul's age = 65 - 44 = 21.

Similarly, Peter's age is (distract (3) from (4)) 65 - 47 = 18.

Check. (1): 18 + 21 = 39 (OK).
       (2): 18 + 26 = 44 (OK).
       (3): 21 + 26 = 47 (OK).
</pre>

This method is standard for solving problems similar to this.
See the lesson <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/The-trick-to-solve-some-word-problems-with-three-and-more-unknowns.lesson>The tricks to solve some word problems with three and more unknowns using mental math</A> in this site.