Final answer:
The number of plants needed when planted 15 cm apart is found through an inverse variation proportion. Given that 75 plants are needed for 20 cm spacing, the solution for the 15 cm spacing is 100 plants.
Step-by-step explanation:
The number of plants used to fill a row of a garden varies inversely as the distance between the plants. If 75 plants are needed when they are planted 20 cm apart, we can find out how many plants are needed when they are planted 15 cm apart by setting up a proportion. We know that the product of the number of plants and the distance between them is constant. Let's denote the number of plants needed for 15 cm apart as x.
So, we have the equation 75 plants * 20 cm = x plants * 15 cm. To solve for x, we do the following:
75 * 20 = 1500
1500 / 15 = 100 plants
Therefore, 100 plants are used to fill the row when planted 15 cm apart.