Question 1020020
Jeff: x
Jay : y
Joseph:z
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x+y = 42
y+z = 59
x+z = 53
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x+y = 42
-
x+z = 53
--------
y-z = -11
~~~~~~~~~~~~~~~~~~~
y+z = 59
+
y-z = -11
------------
2y = 48 divide both sides by 2
y = 24
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Go back to the first equation and substitute for y:
x+y = 42
x+24 = 42
x = 18
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now solve for z, take any one of the equations with z in it and solve it, you'll get the same result. Here's proof:
y+z = 59; 24+z = 59; z = 35
x+z = 53; 18+z = 53; z = 35
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So there you have it:
Jeff: x = 18
Jay : y = 24
Joseph:z = 35
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check: 
Jeff and Jay:18+24 = 42
Jay and Joseph:24+35 = 59
Jeff and Josehp:18+35 = 53
We've got the right answers.
J