Question 1036524
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Hi there,

I was given the following problem and I just can't figure it out. Could you please let me know how to come up with the answer? Thanks!
 
Given these facts: Jack's age plus Marie's age is 27; Jack's age plus Fred's age is 38; Marie's age plus Fred's age is 33. How old is Jack?
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<pre>
Let j, m, f be their ages.  Then

j + m = 27,    (1)
j + f = 38,    (2)
m + f = 33.    (3)

The method to solve this system is as follows.

Add equations (1), (2) and (3) (both left sides and right sides). You will get

2*(j + m + f) = 27 + 38 + 33 = 98,   or

j + m + f = 49.    (4)     ( <<<--- 49 = {{{98/2}}} )

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

f = 49 - 27 = 22.

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

m = 49 - 38 = 11.

Finally, distract equation (3) from (4). You will get

j = 49 - 33 = 16.

<U>Answer</U>.  Jack is 16,  Marie is 11,  and  Fred is 22.
</pre>

The lesson to learn from this solution is this trick for solving this special system of equations.

Actually, &nbsp;it is the method which works in many other similar cases. &nbsp;See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://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> 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Joint-work-word-problems-for-3-4-5-participants.lesson>Joint-work problems for 3 participants</A> &nbsp;(Problem 2)

in this site.