Mathtopia Farm

Mathtopia Farm is one mile long and one mile wide.  Each portion of the farm is dedicated to growing a different crop (as labeled in the picture above).

• Find what fraction of the farm is dedicated to each individual crop.

• Find three crops where the combined land area is equivalent to the land area for two other crops combined.

• Find a combination of crops where the total land area is equivalent to ¾ of the farm’s total area.

• The farmer of Mathopia farm notices that last year’s tomatoes did not make a very good profit. So she has decided to replace the area dedicated to tomatoes with three different spices: oregano, basil, and parsley.
  1. 1. If each of these spices is to receive an equal amount of farmland, what fraction of the farm is dedicated to each of these spices?
  2. 2. If 2/3 of the tomato area is dedicated to basil and 1/3 of the tomato area is dedicated equally to parsley and oregano, what fraction of the farm is dedicated to each of these spices.

Optional:
The farmer of Mathtopia also notices that last year’s potatoes did so well that she now wishes to expand the area dedicated to potatoes by 1/3 of its current area. If the farmer wishes to add on to the current potato area, where could she place this area? How would this affect the other vegetables near the potato? What fraction of the farm would now be dedicated to the potato? To the other vegetables near the potato?