Question 1095287
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<pre>
We are given

M + S = 29,        (1)
S + B = 26,        (2)
B + M = 31.        (3)


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

2M + 2S + 2B = 29 + 26 + 31 = 86.


Divide by 2 both sides of the last equation. You will get

M + S + B = 43.    (4)


Now, subtract eq(1) from eq(4). You will get

B = 43 - 29 = 14.     ====>  Ben is 14 years old.


Next, subtract eq(2) from eq(4). You will get

M = 43 - 26 = 17.     ====>  Matt is 17 years old.


Finally, subtract eq(3) from eq(4). You will get

S = 43 - 31 = 12.     ====> Sam is 12 years old.


<U>Answer</U>.  Sam is the youngest, and he is 12 years old.  Ben is  14 and Matt is 17 years old.


<U>Check</U>.   M + S = 17 + 12 = 29;
         S + B = 12 + 14 = 26;
         B + M = 14 + 17 = 31.
</pre>

Solved.



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To see many other problems, solved by the similar method, look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <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.