Lesson Age problem for three participants

Age problem for three participants

Problem 1

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, subtract equation (1) from (4). You will get

    f = 49 - 27 = 22.


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

    m = 49 - 38 = 11.


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

    j = 49 - 33 = 16.


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