Jim sells hot dogs for $2.95 each and steak sandwiches for $9.95 each out of his food cart. During a busy outdoor festival, he sold a total of 985 items for $7343.75. How many steak sandwiches did he sell?

1. Start with the two equations:

x + y = 985

2.95x + 9.95y = 7343.75

2. Express \( x \) in terms of \( y \) using the first equation:

x = 985 - y

3. Substitute \( x = 985 - y \) in the second equation:

2.95(985 - y) + 9.95y = 7343.75

4. Distribute \( 2.95 \) in the equation:

2905.75 - 2.95y + 9.95y = 7343.75

5. Combine like terms:

2905.75 + 7y = 7343.75

6. Subtract 2905.75 from both sides of the equation:

7y = 4438

7. Divide both sides by 7:

y = 634

Hence, the number of steak sandwiches sold is \( y = 634 \) .