Sam bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 38 cards left. How many cards did Sam start with?

Let x be the number of cards he had at first.

He bought 9 new cards:

x + 9

His dog ate half (Which means he also had half left)

0.5 (x+9)

There are 38 cards left:

0.5 (x+9) = 38

0.5x + 4.5 = 38

0.5x = 38 - 4.5

0.5x = 33.5

x = 33.5 : 0.5

x = 67

So Sam had 67 cards to start off with.

Note: You may want to write 0.5 as half (1/2) ... it is just clumsy to type that, so I kept it as decimal.