math assignment

Math Homework

apportionment

1. A college offers tutoring in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is listed below. If the college can only afford to hire 15 tutors, determine how many tutors should be assigned to each subject. Math: 330 English: 265 Chemistry: 130 Biology: 70.

5. Three people invest in a treasure dive, each investing the amount listed below. The dive results in 36 gold coins. Apportion those coins to the investors. Alice: $7,600 Ben: $5,900 Carlos: $1,400

7. A small country consists of five states, whose populations are listed below. If the legislature has 119 seats, apportion the seats. D: 594,000 E: 211,00

8. A small country consists of six states, whose populations are listed below. If the legislature has 200 seats, apportion the seats. A: 3,411 C: 11,586 E: 3,126

11. A school district has two high schools: Lowell, serving 1715 students, and Fairview, serving 7364. The district could only afford to hire 13 guidance counselors.

Fair Division

1. Chance and Brianna buy a pizza for $10 that is half pepperoni and half veggie. They cut the pizza into 8 slices. If Chance likes veggie three times as much as pepperoni, what is the value of a slice that is half pepperoni, half veggie?

3. Erin, Catherine, and Shannon are dividing a large bag of candy. They randomly split

the bag into three bowls. The values of the entire bag and each of the three bowls in

the eyes of each of the players are shown below. For each player, identify which

bowls they value as a fair share.

Whole Bag Bowl 1 Bowl 2 Bowl 3

Erin $5 $2.75 $1.25 $1.00

Catherine $4 $0.75 $2.50 $0.75

Shannon $8 $1.75 $2.25 $4.00

4. Jenna, Tatiana, and Nina are dividing a large bag of candy. They randomly split the

bag into three bowls. The values of the entire bag and each of the three bowls in the

eyes of each of the players are shown below. For each player, identify which bowls

they value as a fair share.

Whole Bag Bowl 1 Bowl 2 Bowl 3

Jenna $8 $4.50 $0.75 $2.75

Tatiana $4 $1.00 $1.00 $2.00

Nina $6 $1.75 $2.50 $1.75

9. A 6-foot sub valued at $30 is divided among five players (P1, P2, P3, P4, P5) using the

last-diminisher method. The players play in a fixed order, with P1 first, P2 second, and

so on. In round 1, P1 makes the first cut and makes a claim on a piece. For each of the

remaining players, the value of the current claimed piece at the time it is their turn is

given in the following table:

P2 P3 P4 P5

Value of the current claimed piece $6.00 $8.00 $7.00 $6.50

a. Which player gets his or her share at the end of round 1?

b. What is the value of the share to the player receiving it?

c. How would your answer change if the values were:

P2 P3 P4 P5

Value of the current claimed piece $6.00 $8.00 $7.00 $4.50

11. Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items - a

desk and a vanity - using the method of sealed bids. The players' bids (in dollars) are:

A B C D

Desk 320 240 300 260

Vanity 220 140 200 180

a. What is A’s fair share?

b. Find the initial allocation.

c. Find the final allocation