Does one need to worry about the equation coefficients when using pressure?

The Question that I wrote:

C4H10 (g) + O2 (g) CO2 (g) + H2O (g) [unbalanced]

Two closed, rigid vessels are connected by a stopcock. One vessel contains C4H10 with a pressure of 2.34  atm. The other vessel contains O2 with a pressure of 2.96 atm. The experiment is carried out at constant temperature when the stopcock is opened. What is the partial pressure (in Pa) of CO2 when the partial pressure of C4H10 decreases to 0.86 atm?

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My attempt:

C4H10 (g) + 13/2 O2 (g) 4 CO2 (g) + 5 H2O (g)

So, since everything else is constant during the chemical reaction, the moles ratios can be expressed as pressure ratios. Whatever happens to one side of the equation will happen to the other side as well.

C4H10 (g) + 13/2 O2 (g) 4 CO2 (g) + 5 H2O (g)
2.34 atm + 2.96 atm 0 atm + 0 atm   before
0.86 atm                   x atm      after
1.48 atm         =   1.48 atm      change

x = 1.48 atm

I can convert it easily to Pa, but the question is: Do I need to worry about the coefficients of an equation? (ex: Would I need to multiple the pressure by 4?) Did I even do this right? Thanks in advance!