Alexei is stocking a shelf at a store. The shelf can hold 58 cans, so he can still put 39 cans on the shelf before it is full. Create an equation to make sense of the problem and solve it to find out how many cans are already on the shelf. Which equation and answer are correct?

To solve the problem, we need to define the variable \( c \) as the number of cans already on the shelf.

The problem states that the shelf can hold a total of 58 cans, and Alexei can still put 39 cans on the shelf before it is full. This means that the number of cans currently on the shelf plus the number he can still add equals the total capacity of the shelf. This can be expressed with the equation:

\[
c + 39 = 58
\]

Now, we can solve for \( c \):

\[
c = 58 - 39
\]
\[
c = 19
\]

So, the number of cans already on the shelf is 19.

Now let's check the options given:

1. **c - 58 = 39 and 97**: This is incorrect because it does not represent the situation accurately.
2. **c + 39 = 58 and -19**: This is partially correct for the equation part, but -19 is not a valid value for \( c \).
3. **c - 58 = 39 and 97**: This is incorrect for the reasons mentioned in the first option.
4. **c + 39 = 58 and 19**: This is correct for the equation part, and 19 is the right answer for the number of cans currently on the shelf.

Thus, the correct equation is:

\[
c + 39 = 58
\]

and the correct answer is:

\[
c = 19
\]

So, the fourth option is the correct choice.