Solve Mulitfluid Manometer Homework: Find Gage Pressure at Point A

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The discussion revolves around solving a homework problem involving a multi-fluid manometer to find the gage pressure at point A. The relevant equation provided relates the pressure differences to the densities and heights of the fluids involved. The attempted solution suggests that the pressures from the manometer fluids are added to atmospheric pressure while the water pressure is subtracted. There is uncertainty about the correctness of this approach, particularly regarding the treatment of pressures in the equation. Clarification and input on the solution method are sought to ensure accuracy.
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Homework Statement


The manometer shown below measures the pressure of the water in the tank. Using variables for
the densities (no values given), find the gage pressure at point A. Use the symbols ρw, ρ1, and ρ2
for the water and the two manometer fluids.
A picture is attached

Homework Equations


P1-P2=(g/gc)(densitya(h1-h4)+densityb(h3-h2))


The Attempt at a Solution


PA=Patm+ρ2(g/gc)(h3+h2)+ρ1(g/gc)(h2)-ρw(g/gc)(h1)
Im not sure if this is correct or not. Because 1 & 2 have increased pressure going down the tube they were added to Patm and the water had less pressure so it was subtracted. I am not sure if this is right so any input would be great.
 
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here is the manometer picture
 

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