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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 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:

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

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

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