Census Taker
A census taker approaches the man of the house and asks the ages of his children. "I don't know," said the man, "the product of their ages is 72 and the sum of their ages is the house number."
The census taker backed to the sidewalk, looked at the house number and returned to the man saying, "Okay, I still don't know the ages of the children."
"Oh," said the man, "Iforgot to tell you--the oldest one likes chocolate pudding."
The census taker then wrote the ages of the three children. What are the ages of the three children? No, you don't get to know the house number.
Earnings
You talk your board of education into an agreement where you earn 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day, and continually double each day thereafter. How much would you earn at the end of 31 working days?
Magnet School
A
new wing has been added to the Magnet School for Math, Science, and Technology,
so that the student population can be increased by 142 students, 480 to
622. The new sophomore class will have 142 more students than the
graduating senior class. To accommodate the increase, the size of
the faculty is to be increased by seven. There is a great deal of
discussion about which departments should get the extra teachers.
At the time of the increase, the teacher population was:
6 Math
5 English
3 Chemistry
3 Foreign Language(1 Spanish, 1 German, 1 French)
3 Physics
1 Music
4 Biology
1 Art
4 Social Studies
Should every department each receive one teacher, or does the demand on some departments argue that they should receive two new teachers while other departments get none? Should any department get three new members? Given the present number of students taking classes from each department, houw would you apportion the seven new faculty members to departments most fairly? Explain why your decision is fair.
Department
10th 11th
12th Total
Art
21 33
15 69
Biology
198 95
26 319
Chemistry
59 126
109 294
English
183 155
151 489
French
41 32
49 122
German
19 22
10 51
Mathematics
184 201
262 647
Music
20 26
49 95
Physics
50 58
183 291
Social
Studies
183 131
59 373
Spanish
51 26
33 110
Challenge--Army Troop
An army troop 25 miles long begins marching at daybreak. At dusk the troop stops marching. The trooper that began the day at the end of the 25 mile long line has marched 25 miles. Each day a runner begins at the rear of the line and runs to the front of the line and returns to the rear. He repeats this continuously until the troopers camp for the night. How many miles does the runner run in the course of a day? You may not be able to calculate an exact number. Describe your process for solving the problem.