(1) Rectangle: Area and Perimeter
A rectangle has an area of 120 cm2. Its length and width are whole numbers.
Show how you got your answer with explanation and diagrams or table.
a) What are the possibilities for the two numbers?
b) Which possibility gives the smallest perimeter?
(2) Professional Career
Because of the high cost of living, Kimberly, Terry, and Otis each holds down two jobs, but no two have the same occupation. The occupations are doctor, engineer, teacher, lawyer, writer, and painter. Given the following information, determine the occupations of each individual.
· The doctor had lunch with the teacher.
· The teacher and the writer went fishing with Kimberly.
· The painter is related to the engineer.
· The doctor hired the painter to do a job.
· Terry lives next door to the writer.
· Otis beat Terry and the painter at tennis.
· Otis is not the doctor.
(3) Folding Triangles
Triangular Paper Folding Directions: ·
· Cut out a triangular piece of paper. ·
· Fold the triangle through one of its vertices. ·
· Fold the triangle through the same vertex many times. ·
· Each time you fold the paper, record the number of triangles formed by the folds.
Let N = number of folds; T = number of triangles formed by the folds.
0 folds 1 fold 2 folds
1 triangle 3 triangles 6 triangles
a) What pattern did you discover?
b) Find a formula in terms of N that will yield the Nth value of T.
(4) School Sale
The 12th grade class at Manhattan International High School is raffling off a turkey as a moneymaking project.
a) If the turkey cost $22 and raffle tickets are sold for $1.50 each, how many tickets will have to be sold for the class to break even?
b) Create a table to show how many tickets will have to be sold if the class is to make a profit of $20, $50, $100, $200, $n.
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.
(2) Professional Career:
It is given that due to the high cost of living, Kimberly, Terry, and Otis each holds down two jobs, but no two have the same occupation.
We have to find the occupations, doctor, engineer, teacher, lawyer, writer, and painter with respect to their name. We have the following information, to determine the occupations of each individual.
(i) The doctor had lunch with the teacher. Hence doctor and teacher are different person.
(ii) The teacher and the writer went fishing with Kimberly. Hence Kimberly is neither a teacher nor a writer.
(iii) The painter is related to the engineer. Hence one who is painter is also engineer.
(iv) The doctor hired the painter to do a job. Hence one who is doctor not a painter.
(v) Terry lives next door to the writer. Hence Terry is not a writer.
(vi) Otis beat Terry and the painter at tennis. Hence Otis and Terry are not painter .
(vii) Otis is not the doctor.
It is clear from above discussion that Kimberly, Terry, and Otis are three persons.
As Kimberly, Terry, are not writer so Otis is the writer.
Also Kimberly, and Otis, are not doctor so Terry is the doctor.
And Kimberly is not teacher, writer and engineer. So from above
Kimberly is painter and lawyer.
Otis is the writer and teacher.
Terry is the doctor and engineer....