Answer
See the answer below.
Work Step by Step
Assuming that the temperature remains constant:
$n_{He}=P_1V_1/RT$
$n_{Ar}=P_2V_3/RT$
$n_{He}+n_{Ar}=P_f(V_1+V_2)/RT=P_1V_1/RT+P_2V_2/RT$
$P_f=(P_1V_1+P_2V_2)/(V_1+V_2)$
$P_f=229\ mmHg$
$P_{He}=P_1V_1/(V_1+V_2)=87\ mmHg$
$P_{Ar}=P_2V_2/(V_1+V_2)=142\ mmHg$
