Here's how I go about doing this.

What we can do is use the *ideal gas equation* for both #"Ar"# and #"O"_2# to find the total moles. Then we use the ideal gas equation a third time to find the total pressure with known total moles, volume (#400# #"mL"#) and temperature (#24^"o""C"#).

I won't show the unit conversions here, as I predict you already know how; the moles of each substance is

#n_ "Ar" = ((1.47cancel("atm"))(0.600cancel("L")))/((0.082057(cancel("L")•cancel("atm"))/("mol"•cancel("K")))(494cancel("K"))) = 0.0218# #"mol Ar"#

#n_ ("O"_2) = ((0.580cancel("atm"))(0.200cancel("L")))/((0.082057(cancel("L")•cancel("atm"))/("mol"•cancel("K")))(388cancel("K"))) = 0.00365# #"mol O"_2#

#n_"total" = 0.0218# #"mol Ar"# #+ 0.00365# #"mol O"_2# #= 0.0254# #"mol"#

We'll now use the ideal gas equation to solve for the pressure at the new conditions:

#P = (nRT)/V = ((0.0254cancel("mol"))(0.082057(cancel("L")•"atm")/(cancel("mol")•cancel("K")))(297cancel("K")))/(0.400cancel("L"))#

#= color(blue)(1.55# #color(blue)("atm"#