To determine the number of additional purple marbles needed for half of the total marbles to be purple, we first need to calculate half of the total number of marbles.
Total number of marbles = 20 white marbles + 40 purple marbles + 50 yellow marbles = 110 marbles
Half of the total marbles = 110 marbles / 2 = 55 marbles
Since the son wants half of the marbles to be purple, we subtract the current number of purple marbles from half of the total marbles:
Number of additional purple marbles needed = 55 marbles - 40 purple marbles = 15 marbles
Therefore, Santa Claus needs to add 15 more purple marbles to the 110 marbles he already has until half of them are purple.
