Let's analyze the problem step by step.
The total capacity of the shelf is 58 cans. Alexei can still put 39 more cans on the shelf before it is full. This means the number of cans already on the shelf (let's denote it as \(c\)) plus the 39 cans he can still add equals the total capacity of the shelf (58 cans).
So, we can set up the equation: \[ c + 39 = 58 \]
Now we will solve for \(c\) (the number of cans already on the shelf):
- Subtract 39 from both sides of the equation: \[ c = 58 - 39 \]
- Calculate the right side: \[ c = 19 \]
Thus, the number of cans already on the shelf is 19.
The correct equation and answer from the options provided is: c + 39 = 58 and 19.