WASHINGTON STATE MATHEMATICS COUNCIL 1999 MIDDLE SCHOOL MATH OLYMPIAD FIFTH GRADE SESSION I : THE MONKEY DIET PROBLEM 5

Monkeys in a zoo each need exactly 4000 calories a day to stay healthy. Also to stay healthy, they need to get:

• From 800 to 1200 calories from fat,

• From 800 to 1200 calories from protein,

• From 1600 to 2400 calories from carbohydrates.

Their 3 main foods are bananas, eggs, and coconuts. Here is a table showing the cost of these foods, the calories, and the sources of the calories.

 FOOD Cost Each Calories Each Calories from Fat Calories from Protein Calories from Carbohydrates Bananas \$0.15 100 10 0 90 Eggs \$0.10 100 20 80 0 Coconuts \$2.00 1000 300 200 500

Your task is to plan the daily diet for your monkeys. Each monkey gets a whole number of each item per day. (For example, you cannot give a monkey half of a coconut.) Furthermore, the zoo director is interested in keeping costs low, so you should check more than one diet to find out which one has the lowest cost.

HERE ARE YOUR INSTRUCTIONS:

1. Find at least two diets that meet the needs of the monkeys and recommend the lowest cost diet to the zookeeper.
2. Show us your work. Show us what patterns you noticed in solving this problem. Tell us about the strategy you used. Explain all of the step in your reasoning using sentences, pictures or tables. Tell us how you know your answer is reasonable.