Finding an unknown charge in a system of discrete point charges.

[Zift]

A point particle that has a charge of 15.0 µC is located at x = 0, y = 0 (we'll call it q₀ and a point particle that has a charge q is located at x = 12.0 cm, y = 0 (we'll call it q₁. The electric force on a point particle that has a charge of 6.0 µC at x = 24.0 cm, y = 0 is -(19.7) N $$\hat{i}$$ (we'll call it q₂. When this 6.0-µC charge is repositioned at x = 17.8 cm, y = 0, the electric force on it is zero. Determine the charge q.

First I tried to equate the electric force on q₂ to the vector of the forces on q₂ due to q₀ and q₁ using coulomb's law and then solve for q₁, but this does not yield the correct value. I have been able to do all the other problems in the section on discrete charge distributions, but I'm completely stumped on this one. I also tried to do the same procedure but with the electric force on q₂ equal to zero as indicated in the last sentence and but its yields a different (and still incorrect) value. what am I doing wrong. Am i missing something? Is there crucial information I should be deriving from the last sentence?

 

[ehild]

This problem looks over-defined, and I also found the results controversial.

ehild