SOLUTION: 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

Let Jack's age, be J

Then Marie's is: 27 - J, and Fred's is: 38 - J

Also, 27 - J + 38 - J = 33

- J - J + 65 = 33 

- J - J = 33 - 65 

- 2J = - 32

J, or Jack's age is = , or  

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 =  )

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.

Answer.  Jack is 16,  Marie is 11,  and  Fred is 22.