WASHINGTON STATE MATHEMATICS COUNCIL 1999 MIDDLE SCHOOL MATH OLYMPIAD SIXTH GRADE SESSION I : THE MONKEY DIET PROBLEM 6

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

• From 20% to 30% calories from fat,

• From 20% to 30% calories from protein,

• From 40% to 60% 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 30% 20% 50%

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.