Billy has a collection of baseball cards that he has separated into two different value categories. his common cards are worth $0.50 each, while his premium cards are worth $1.00 each. together, billy’s entire baseball card collection of 124 cards is worth $81.50.

Let Billy have x common cards, and y premium cards:

(i) Billi has 124 cards:

       x+y=124

(ii) the total value of the cards is 81.50$:
 
       0.5x $ + 1.00*y $= 81.50 $, so

       0.5x+y=81.5

we can write y=81.5-0.5x and substitute in (i):

x+y=124
x+(81.5-0.5x )=124
x+81.5-0.5x=124

x-0.5x=124-81.5
0.5x=42.5

x=42.5/0.5=85

y=124-85=39

Billy has 85 common cards and 39 premium cards