WASHINGTON STATE MATHEMATICS COUNCIL - 1997 MIDDLE SCHOOL MATH OLYMPIAD

GRADES 7 AND 8 SESSION I - PROBLEM SOLVING

Tom and Cheryl Thornton are preparing a large display for their fruit trees and berries at Cloud Mountain Nursery. They want to devote no more than 140 square feet in front of the nursery for the display. There will be four displays and they need to be separated by at least 2 feet in order for people to walk between them. Each area will be surrounded by a border of timbers. Tom says they have exactly 86 feet of border material credited at the lunber store from another job.

Display Requirements:
• The apple trees display will have an area of 24 square feet with a width of 3 feet.
• The pear trees display will have an area of 24 square feet, and a width greater than 3 feet.
• The berries display will have an area of 24 square feet and a width less than 3 feet.
• The kiwi trees will have an area that is 2/3 the area of the others. The length of its perimeter happens to have exactly the same magnitude as its area.

The Thorntons want to hire a contractor to design their nursery display and build the borders. They have an account at Higher Plane Lumber Company with 86 feet of border timbers left over from another job. The timbers come in only 8 feet, 10 feet, and 12 feet lengths. The Thornton's want the sides to be whole numbers of feet long (no fractions.) Your job is to design a layout for the displays. Tom thinks it is possible to build all of the displays without purchasing any more material. The more efficient use of space, the more Tom and Cheryl will be pleased.

Cheryl is hoping your team will provide at least three important details in your solution:
• A plan (scaled map) of the area to be used for the fruit trees and berries, complete with dimensions
• A list of materials that they will need from the lumber store, and what each display needs for materials.
• A convincing reason why your team's plan is the best fit for the design.

You have one hour to work this problem.