Final answer:
After setting up and solving two algebraic equations, we find that Kevin has 33 baseball cards and Josh has 45 baseball cards.
Step-by-step explanation:
To solve the problem we need to set up two equations based on the information given. Let x represent the number of cards Kevin has and y represent the number of cards Josh has. We know that together they have 78 cards, so our first equation is x + y = 78. We also know that Josh has 12 more cards than Kevin, which gives us the second equation: y = x + 12.
First, substitute y from the second equation into the first equation:
- x + (x + 12) = 78
- 2x + 12 = 78
- 2x = 78 - 12
- 2x = 66
- x = 66 / 2
- x = 33
Now that we know Kevin has 33 cards, we can find out how many cards Josh has by placing x into the second equation:
- y = x + 12
- y = 33 + 12
- y = 45
Therefore, Kevin has 33 baseball cards and Josh has 45 baseball cards.