Washington State Math Council
Middle School Math Olympiad 1997

You have just bought a home in the country which has space for a garden! The space is 1 acre in size. (1 acre = 43,560 square feet). You want to plant some good things to eat. You go to the seed store and find this list of vegetables and how much land is covered by each sack of seed.




5000 sq. ft.

Soybeans 8750 sq. ft.


7250 sq. ft.

Green beans

6250 sq. ft.


7310 sq. ft.

You can only buy whole sacks of seeds. You are a very thrifty farmer and don't want to waste seed!

Your job is to plan your garden. Decide what vegetables you want to plant and how many sacks of seed you need of each vegetable so that you plant as much of your 1 acre as you can and have as little seed as possible left over. You don't have to plant every vegetable.
The best solution will fill the whole garden and have no seed left over.

Your response should be made on the Response Sheet in 3 parts:

  1. Restate the problem in your own words. (Mention 4 things about the problem for a top score.)
  2. Investigate the problem. Try different solutions. (Compare and describe 2 or more different complete answers for a top score.) Show us your work. Use the back of the response sheet if you need more room.
  3. Conclusion. Tell us how many sacks of each vegetable you want to plant. (For a top score, your solution should use all of the available farmland and state a reason for selecting it.)

You have 40 minutes to complete the problem.
Link to the Response Sheet