Flux through sphere from six point charges using Gauss's law

[Kyho]

Hi, got some homework to do in electromagnetism and one of the problems is:

Homework Statement

Consider a Cartesian coordinate system with charges Q (Q = 15μC) at x = + and – 1.3cm, and at y = + 1.7cm and
– 0.7cm and at z = + 2cm and -0.5cm. Calculate the flux of the electrostatic field through the surface of a sphere
of radius 3cm, centered at the origin.

Equations:
Gauss law. Coulomb law

Attempts:
I don't really know the right way to start this problem. The only thing I done is placed the charges in a cartesian coordinate system. I thought of calculating all the electric fields to get the resultant electric field. and from there on I have no idea how to continue.

Not asking here for a complete solution of the problem, but maybe a hint on how to start.

 

[granpa]

think of the flux lines as flowing water. the charges are sources of water. calculate the total amount of water leaving the sphere.

 

[Kyho]

well after consulting with some friends, they came to the result that you just got to add up the charges and the divide it through epsilon0. (thanks to: superpostion principle)

seems a bit to simplictic for an uni exercise sheet as the one from last week was way harder :/.