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:
$P = (nRT)/V = ((0.0254cancel("mol"))(0.082057(cancel("L")•"atm")/(cancel("mol")•cancel("K")))(297cancel("K")))/(0.400cancel("L"))$
$= color(blue)(1.55$ $color(blue)("atm"$