Washington State Math Council
Middle School Math Olympiad 1997
THE FARMER PROBLEM--Grade 6

You have just bought a home in the country which has 10 acres of farm land. (1 acre = 43,560 sq. ft.) You want to plant vegetables on your farm, so you drive to the Farmville Feed Store to buy seed. On the wall at the feed store is this list of vegetables, the weight of each sack of seed, and how much area a sack covers.

VEGETABLE

EACH SACK WEIGHS

EACH SACK COVERS

Corn

100 pounds

10,000 sq. ft.

Soybeans

100 pounds

85,000 sq. ft.

Squash

50 pounds

32,500 sq. ft.

Green beans

75 pounds

22,500 sq. ft.

Peas

75 pounds

13,100 sq. ft.



You can only buy whole sacks of seeds. You are a very thrifty farmer and don't want to waste seed! You drove to Farmville in a pickup truck which can carry 1000 pounds. Farmville is a long way from your farm, so you want to take all your seed back in only 1 trip. So, the total weight of all your seed must not exceed 1000 pounds.

Your job is to plan your farm. 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 10 acres as you can and have as little seed as possible left over. It must all fit in a 1000 pound pick-up truck. You don't have to plant every vegetable. The best solution fills 10 acres with no seed left over and weighs 1000 pounds or less.

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

  1. State 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 and how much it all weighs. (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