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?
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
Let x, y , z represent Peter, Paul and Mary's age
Question States***(Write as You Read)
I. x + y = 39
II.x + z = 44 Subtracting 1st from second
z-y = 5
III. y+z = 47 0r
z-y = 5
z + y = 47
2z = 52
z = 26, x = 18  and y = 21 
Answer by ikleyn(52805)  (Show Source):
You can put this solution on YOUR website! .
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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).
This method is standard for solving problems similar to this.
See the lesson The tricks to solve some word problems with three and more unknowns using mental math in this site.
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