To determine how many hockey cards Dave has to start, let's start from the bottom.
a.) Charlotte gave Johnnie half of the cards she received from Dave.
Johnnie kept 8 of those cards.
He gave the remaining 10 to Dana.
Total number of cards Johnnie received = 8 + 10 = 18 hockey cards
Johnnie received 18 hockey cards from Charlotte.
Thus, for Charlotte:
No. of cards Charlotte received ÷ 2 = No. of cards Johnnie received
No. of cards Charlotte received = No. of cards Johnnie received x 2
No. of cards Charlotte received = 18 x 2 = 36 hockey cards
Therefore, Charlotte received 36 hockey cards from Dave.
b.) Dave gave Charlotte half of his hockey cards.
No. of cards Dave has ÷ 2 = No. of cards Charlotte received
No. of cards Dave has = No. of cards Charlotte received x 2
No. of cards Dave has = 36 x 2 = 72 hockey cards
Therefore, originally, Dave has 72 hockey cards from the start.
The answer is 72 hockey cards