SOLUTION: David and Alex have a total of 25 years. John is 10 years older than David. How old is Alex if 5 year from now, John will be 16 years old?

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Question 1113756: David and Alex have a total of 25 years. John is 10 years older than David. How old is Alex if 5 year from now, John will be 16 years old?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
David and Alex have a total of 25 years. 
(1)     D + A = 25

John is 10 years older than David. 
(2)     J = D + 10

5 years from now, John will be 16 years old. 
(3)     J + 5 = 16

How old is Alex?
Solve (3)

       J + 5 = 16
           J = 11

Substitute 11 for J in (2)

       J = D + 10
      11 = D + 10
       1 = D

Substitute 1 for D in (1)

       D + A = 25
       1 + A = 25
           A = 24

Alex is 24.

---------------

Checking:  A = 24, D = 1, J = 11

David and Alex have a total of 25 years. 
That checks because 1 + 24 = 25

John is 10 years older than David. 
That checks because 11 = 1 + 10

How old is Alex if 5 year from now, John will be 16 years old?
That checks because 11 + 5 = 16.

Edwin
Answer by ikleyn(52879)   (Show Source): You can put this solution on YOUR website!
.
"If 5 year from now, John will be 16 years old", it means that John is 11 years now.


Since "John is 10 years older than David", it implies that David is 1 year old now.


Since "David and Alex have a total of 25 years", it implies that Alex is 24 years old.


3 lines mental solution.


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I am sure that this problem is EITHER for young students (2nd - 3rd grades) who still know nothing about systems of linear equations,
OR for quite old  (70 years and older)  who use it as the therapy and logical exercises for their minds.



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