If the gardener can fill the border with 30 flowers planted 12 inches apart, how far apart should the gardener plant 36 flowers instead?

10 inches

Step-by-step explanation:

This inversely proportional function, the more flowers - the less distance.

Flowers = k/distance

30 = k/12

k = 30*12 = 360

Flowers = 360/distance

New number of flowers and new distance:

Flowers = 360/distance

36 = 360/distance

distance = 360/36 = 10 (inches)