A gardener will use up to 250 square feet for planting flowers and vegetables. He wants the area used for vegetables to be at least four times the area used for flowers.

Question

A gardener will use up to 250 square feet for planting flowers and vegetables. He wants the area used for vegetables to be at least four times the area used for flowers. Let denote the area (in square feet) used for flowers. Let denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of and that satisfy these requirements.

Answer 1

I'll use F for flower area and V for veggies.

F + V = 250

Also, V ≥ 4F substitute for V:

F + 4F = 250

5F = 250

F = 50, so V ≥ 4(50) or 200 sq.ft. You would shade 1/5th of the area for flowers and 4/5ths for veggies.