Answer
This is not the correct method, because it does not produce a 0.500M solution.
Work Step by Step
Volume after reaction: 50 ml + 250 ml = 300 ml
1. Find the concentration after the dilution:
$C_1 * V_1 = C_2 * V_2$
$0.250*250= C_2 *300$
$62.5 = C_2 *300$
$C_2 =0.208M$