Final answer:
To calculate how many plants there are in total, use the formula 4x - 4 (for the perimeter) and add 20 (leftover). For additional plants, find the smallest square number larger than the total number of existing plants; the difference is the number of plants to add.
Step-by-step explanation:
To solve the problem mathematically, let's consider that the square garden has sides of length 'x'. Since 15 plants are planted along each side, the total number of plants required for the perimeter would be 4 times 15, minus the four corner plants that are double-counted, so the formula is 4x - 4. Then we also know that after planting these there are 20 plants left.
Therefore, the equation would be 4x - 4 + 20 = total number of plants. However, the student also asks for the smallest number of plants that can be added so that all can be planted in the garden, which leads to find the next perfect square number after the total amount of plants first calculated. This is because the square number will allow them to have a full square planting without leftovers.
Let n be the total number of plants already existing. If y is the side length of the new square garden considering the additional plants, then y^2 should be the smallest square number larger than n. The number of plants to add would be y^2 - n.