## Wednesday, January 31, 2007

### Puzzling: Entomology Problems

Title: Entomology - The Problems
Date: 01/01/07

The Problems

Entomology is the scientific study of insects. Jung, Tara and Pavan collected some insects for their science project. At the end of the first week of collecting Jung and Tara together had 26 insects, Tara and Pavan together had 18 insects, and Pavan and Jung together had 22 insects. How many insects did each person have alone?

The number of insects they had in their collection continuously changed throughout the second week as they worked to improve the quality and variety of the insects in their collection. They took some insects out and added other new insects. The difference between the maximum and minimum number of insects they had in their collection during the second week of collecting was 38. The mean of the maximum and minimum number of insects in the collection during the second week of collecting was 46. What was the maximum and minimum number of insects in the collection during the second week of collecting?

At the end of the third week of collecting they divided their collection of insects into 3 categories: winged, more than one color, and length less than one-half inch.

2 insects were winged, more than one color, and less than one-half inch long

7 insects (of various lengths) were winged and more than one color

6 insects (winged and non-winged) were more than one color and less than one-half inch long

5 insects (of single and multi-colorings) were winged and less than one-half inch long

12 insects were less than one-half inch long, non-winged, and only brown

9 insects were winged, more than one-half inch long, and only brown

14 insects were more than one color, more than one-half inch long, and non-winged

5 insects did not have any of the sorted characteristics

How many insects were in their collection at the end of the third week of collecting?

1. SPOILER

http://clipmarks.com/clipmark/7B5AE415-0208-4E68-AF9A-1D6EA8D58EA8/

2. t = Tara
p = Pavan
j = Jung

t+p=18
j+t=26
p+j=22

p=18-t
j=26-t

26-t + 18-t = 22
44-2t=22
-2t=-22
t=11
if t=11, then j=26-11=15
and p = 18-11 = 7

So Pavan has 7 bugs; Tara has 11 bugs, and Jung has 15 bugs.

3. Problem #2

Range = max-min = 38

mean = 46

38÷2=19

46+19=65
46-19=27

So the greatest number of bugs they had was 65 and the least number of bugs they had was 27.